The Accuracy of Electron Density from Theory : Calculating Electric Field Gradients and X-ray Scattering for Molecules and Solutions

Abstract

Electron density is the principle determinant of the characteristic properties of molecules, their structure and dynamics. For this reason it is vital to ascertain accurate densities. One method of predicting electron densities is density functional theory (DFT). It is derived from the Hohenburg-Kohn theorem which states that an exact ground-state energy should yield an exact electron density and vice versa. In reality the exact solution is not fully known as exchange and correlation have to be estimated. Were it known, accurate densities and energies could be calculated at a fraction of ab initio computational cost. However, it is noted that functional methods have deviated from the path to the exact functional due to energetic overfitting. This study used the electric field gradient (EFG) as an electron-density probe to facilitate comparison both to ab initio calculation (CCSD(T)) and microwave spectroscopy for simple transition metal complexes and halogenated aromatic compounds. EFGs improved with increased Hartree-Fock (HF) exchange fraction encountered for higher rungs of Jacob’s Ladder due to selfinteraction error (SIE) reduction. SIE cancellation was uneven between transition metals, halogens and aromatic rings, causing functional-dependent electronegativity. Electron density can also be inferred from X-ray scattering. X-ray free-electron lasers (XFELs) are used to probe molecular structure and dynamics on ultrafast time scales. Solutions contains additional scattering signals other than the desired solute from the solvent and solutesolvent. The solvent term can be extracted experimentally or via molecular dynamics (MD) trajectories. Theory is also the only method of predicting the solute-solvent term independently. The solvent force-field parameters can be derived from experiment or theoretically from DFT calculation. The impact of the chosen force field on the the predicted scattering profiles was evaluated herein, Quantum Bespoke Kit (QUBE) and all-atom Optimised Potentials for Liquid Simulations (OPLS-AA) force-fields were used to assess theoretically- and experimentally-derived parameters respectively for common solvents for the same test solute (I2). Force-field dependence is elucidated for both terms due to differences in non-bonded parameters.There also remains further investigation to better approximate experimental solvent terms. Solute-solvent scattering occurs on comparable scales to the solute scattering. XFELs have also been applied recently to improve understanding metal-to-ligand charge transfer (MLCT) in transition metal complexes and the influence of polar solvents in their structures. QUBE was used to investigate the ground and excited states of [Cu(phen)2]+ and compared to recent classical MD and quantum-mechanical/molecular mechanical (QM/MM) simulations. It performed particularly well in regards to identifying Cu-N bond asymmetry and solvent influence in the ligand-ligand dihedral in the triplet state which were not identified in previous theoretical investigation but in agreement with recent experimental understanding. This improvement was attributed to its use of high-rung DFT in parameterisation (wB97X-D). Overall this investigation evaluate thoroughly the current state of theory in reproducing accurate electron densities, highlighting the importance of reducing DFT SIE to improve density accuracy, which in turn impacts force-field parameter quality, indicating that DFT improvement impacts all branches of theoretical chemistry.