The dynamics of a molecule in a magnetic field is significantly different from its zero-field counterpart. One important difference in the presence of a field is the Lorentz force acting on the nuclei, which can be decomposed as the sum of the bare nuclear Lorentz force and a screening force due to the electrons. This screening force is calculated from the Berry curvature and can change the dynamics qualitatively. It is therefore important to include the contributions from the Berry curvature in molecular dynamics simulations in a magnetic field. In this work, we present a scheme for calculating the Berry curvature numerically using a finite-difference technique, addressing challenges related to the arbitrary global phase of the wave function. The Berry curvature is calculated as a function of bond distance for H 2 at the restricted and unrestricted Hartree-Fock levels of theory and for CH + as a function of the magnetic field strength at the restricted Hartree-Fock level of theory. The calculations are carried out using basis sets of contracted Gaussian functions equipped with London phase factors (London orbitals) to ensure gauge-origin invariance. In this paper, we also interpret the Berry curvature in terms of atomic charges and discuss its convergence in basis sets with and without London phase factors. The calculation of the Berry curvature allows for its inclusion in ab initio molecular dynamics simulations in a magnetic field.

The guanidine–quinoline ligand dimethylethyleneguanidinoquinoline (DMEGqu) is able to stabilise bis(chelate) copper complexes in an intermediate geometry between tetrahedral and square‐planar environments. The structures of the obtained complexes model the entatic state and have been investigated in solid state by single‐crystal X‐ray diffraction and in the solid state and in solution by X‐ray absorption spectroscopy. The dimethylethyleneguanidine (DMEG) unit of the DMEGqu ligand displays a smaller steric encumbrance than the tetramethylguanidine (TMG) counterpart; this allows slightly larger structural changes upon oxidation than those for the TMG counterparts. Moreover, triflate coordination was possible for the CuII DMEG complexes. DFT analyses revealed that good structural and optical descriptions are possible through the use of the hybrid functionals B3LYP and TPSSh in combination with the triple‐zeta basis set def2‐TZVP and the inclusion of empirical dispersion with Becke–Johnson damping and a suitable solvent model. The orbital analysis gives insights into the electronic structure of the complexes and their charge‐transfer behaviour.

The electron-transfer abilities of the copper guanidinoquinoline (GUAqu) complexes [Cu(TMGqu) ] and [Cu(DMEGqu) ] (TMGqu=tetramethylguanidinoquinoline, DMEGqu=dimethylethylguanidinoquinoline) were examined in different solvents. The determination of the electron self-exchange rate based on the Marcus theory reveals the highest electron-transfer rate of copper complexes with pure N-donor ligands (k =1.2×10 s m in propionitrile). This is supported by an examination of the reorganisation energy of the complexes by using Eyring theory and DFT calculations. The low reorganisation energies in nitrile solvents correspond with the high electron-transfer rates of the complexes. Therefore, the [Cu(GUAqu) ] complexes act as good entatic states model of copper enzymes. The structural influence of the complexes on the kinetic parameters shows that the TMGqu system possesses a higher electron-transfer rate than DMEGqu. Supporting DFT calculations give a closer insight into the kinetics and thermodynamics (Nelsen's four-point method and isodesmic reactions) of the electron transfer.

We explore and show the usefulness of the density of states function for computing vibrational free energies and free energy differences between small systems. Therefore, we compare this density of states integration method (DSI) to more established schemes such as Bennett’s Acceptance Ratio method (BAR), the Normal Mode Analysis (NMA), and the Quasiharmonic Analysis (QHA). The strengths and shortcomings of all methods are highlighted with three numerical examples. Furthermore, the free energy of the ionization of ammonia and the mutation from serine to cysteine are computed using extensive ab initio molecular dynamics simulations. We conclude that DSI improves upon the other frequency-based methods (NMA and QHA) regarding the treatment of anharmonicity and yielding results comparable to BAR in all cases without the need for alchemical transformations. Low-frequency modes lead to larger errors indicating that long simulation times might be required for larger systems. In addition, we introduce the use of DSI for the localization of the vibrational free energy to specific atoms or residues, leading to insights into the underlying process, a unique feature that is only offered by this method.