Gaussian approximation potentials: Theory, software implementation and application examples.

Gaussian Approximation Potentials (GAPs) are a class of Machine Learned Interatomic Potentials routinely used to model materials and molecular systems on the atomic scale. The software implementation provides the means for both fitting models using ab initio data and using the resulting potentials in atomic simulations. Details of the GAP theory, algorithms and software are presented, together with detailed usage examples to help new and existing users. We review some recent developments to the GAP framework, including Message Passing Interface parallelisation of the fitting code enabling its use on thousands of central processing unit cores and compression of descriptors to eliminate the poor scaling with the number of different chemical elements.

Self-Consistent Implementation of Hybrid Functionals with Local Range Separation.

Building on the previously introduced concept of local range separation (LRS) [ Krukau , A. V. ; Scuseria , G. E. ; Perdew , J. P. ; Savin , A. Hybrid functionals with local range separation J. Chem. Phys. 2008 129 124103 ], we report the first self-consistent implementation of hybrid exchange functionals with a position-dependent range-separation parameter. The two-electron integrals emerging from long-range exact exchange are calculated seminumerically. This avoids formerly suggested approximations to the exact exchange part and paves the way for applications to larger and chemically relevant systems. Additionally, we investigate the role of short-range exchange in this LRS scheme by comparing the local density approximation and PBE-type functionals. We propose a semiempirical approach for the range-separation function based on common ingredients of semilocal exchange-correlation functionals. Four parameters are optimized to a small training set of atomization energies and barrier heights. In comparison with established hybrid and semilocal functionals, the LRS functional performs well for basic chemical properties. In addition, our best functional yields outer-valence spectra comparable to optimally tuned approaches.

MVO-10: A Gas-Phase Oxide Benchmark for Localization/Delocalization in Mixed-Valence Systems.

Ten simple gas-phase, main-group as well as transition-metal, mixed-valence (MV) oxo complexes are suggested for the screening of electronic-structure methods for the computational study of localization vs delocalization of charge and spin density in MV systems, without the usual added complication of environmental effects. Benchmark coupled-cluster energies up to CCSDT(Q)/CBS (for Al2O4-, Si2O4+, Si2O4-, ScO2, TiO2+) and CCSD(T)/CBS (for Ti2O4-, Ti2O4-, V2O4+, Cr2O6-) quality are provided as a basis for screening a variety of density-functional methods, ranging from a generalized gradient approximation via global and range-separated to local hybrid functionals. Additionally, experimental evidence for a delocalized D2d structure of the somewhat larger V4O10- is used. None of the functionals is fully satisfactory when tasked with describing simultaneously the most extreme cases, the localized Al2O4- and the delocalized V4O10-. While relatively large exact-exchange admixtures are required for the former, and for related localized cases, lower ones are preferable for the latter, as well for other delocalized d1d0 systems. The overall best combined performance is provided by a Lh-SVWN (g(r) = 0.670 τW/τ) local hybrid, the MN15 global hybrid, and the ωB97X-D range-separated hybrid. We also provide vibrational data for comparison with experiment.

Implementation of Molecular Gradients for Local Hybrid Density Functionals Using Seminumerical Integration Techniques.

We present the first implementation of the derivative of the local hybrid exchange-correlation energy with respect to the displacement of nuclei in a Gaussian-type atomic basis set. This extends a recent efficient implementation of local hybrid functionals for self-consistent Kohn-Sham and linear-response TDDFT calculations into the TURBOMOLE program package. In contrast to seminumerical schemes for global exact-exchange admixtures and to the related SCF and TDDFT implementations of local hybrid functionals, additional analytical integrals have to be evaluated at each grid point in the case of molecular gradients. The overall efficiency of the present scheme is improved through prescreening with the density matrix (P-junctions), as well as with spherical overlap estimates (S-junctions). Comparative timings for structure optimizations with local vs global hybrid functionals are discussed while gauging the accuracy for S- and P-junctions using varying thresholds. Local hybrids are furthermore assessed for structure optimization and harmonic vibrational frequency calculations (using numerical second derivatives) of a selection of test systems, comparing with experimental data and some widely used density functionals.

Electron transfer pathways in mixed-valence paracyclophane-bridged bis-triarylamine radical cations.

A series of paracyclophane (PC) bridged mixed-valence (MV) bis-triarylamine radical cations with different ([2.2], [3.3], [4.4]) linkers, with and without additional ethynyl spacers, have been studied by quantum-chemical calculations (BLYP35-D3/TZVP/COSMO) of ground-state structures, thermal electron-transfer barriers, hyperfine couplings, and lowest-lying excited states. Such PC-bridged MV systems are important intra-molecular model systems for inter-molecular electron transfer (ET) via π-stacked aromatics, since they allow enforcement of a more or less well-defined geometrical arrangement. Closely comparable ET barriers and electronic couplings for all [2.2] and [3.3] bridges are found for these class-II MV systems, irrespective of the use of pseudo-para and pseudo-meta connections. While the latter observation contradicts notions of quantum interference for off-resonant conduction through molecular wires, it agrees with the less intricate nodal structures of the highest occupied molecular orbitals. The ET in such MV systems may be more closely connected with hole conduction in the resonant regime. Computations on model cations, in which the [2.2] linkers have been truncated, confirm predominant through-space π-π electronic coupling. Systems with [4.4] PC bridges exhibit far more structural flexibility and concomitantly weaker electronic interactions between the redox centers.