Benchmarking of the <i>R</i>^–7 Anisotropic Dispersion Energy Term on the S22 Dimer Test Set

The effects of including the anisotropic <i>E</i>₇ term to the dispersion energy in addition to the leading <i>E</i>₆ term are examined by using the effective fragment potential (EFP) method on the S22 test set. In this study, the full anisotropic <i>E</i>₇ term is computed whereas the isotropic and spherical approximations are used for the <i>E</i>₆ term. It is found that the <i>E</i>₇ term is positive for hydrogen-bonded complexes and has a magnitude that can be as large as 50% of <i>E</i>₆, giving rise to larger intermolecular distances than those obtained with <i>E</i>₆ alone. The large positive value of <i>E</i>₇ is analyzed for the hydrogen-bonded uracil dimer; it is found to originate from the large magnitude of the dynamic polarizability tensors as well as the proximity of the LMOs involved in hydrogen bonding. Conversely, <i>E</i>₇ tends to be negative for dispersion-dominant complexes, and it has a very small magnitude for such complexes. The optimized geometries for these systems are therefore not greatly affected by the presence of the <i>E</i>₇ term. For the mixed systems in the S22 test set, an intermediate behavior is observed. Overall, the <i>E</i>₇ term is most important for systems with hydrogen bonding interactions and mixed systems. A full anisotropic treatment of the <i>E</i>₆ term and higher order terms may need to be included to obtain more accurate interaction energies and geometries

Benchmarking the Effective Fragment Potential Dispersion Correction on the S22 Test Set

The usual modeling of dispersion interactions in density functional theory (DFT) is often limited by the use of empirically fitted parameters. In this study, the accuracies of the popular empirical dispersion corrections and the first-principles derived effective fragment potential (EFP) dispersion correction are compared by computing the DFT-D and HF-D equilibria interaction energies and intermolecular distances of the S22 test set dimers. Functionals based on the local density approximation (LDA) and generalized gradient approximation (GGA), as well as hybrid functionals, are compared for the DFT-D calculations using coupled cluster CCSD­(T) at the complete basis set (CBS) limit as the reference method. In general, the HF-D­(EFP) method provides accurate equilibrium dimerization energies and intermolecular distances for hydrogen-bonded systems compared to the CCSD­(T)/CBS reference data without using any empirical parameters. For dispersion-dominant and mixed systems, the structures and interaction energies obtained with the B3LYP-D­(EFP) method are similar to or better than those obtained with the other DFT-D and HF-D methods. Overall, the first-principles derived -D­(EFP) correction presents a robust alternative to the empirical -D corrections when used with the B3LYP functional for dispersion-dominant and mixed systems or with Hartree–Fock for hydrogen-bonded systems

Theoretical Investigation of Relaxation Dynamics in Au₃₈(SH)₂₄ Thiolate-Protected Gold Nanoclusters

A subtle change in the electronic structure of thiolate-protected noble metal nanoparticles can result in distinctive energy relaxation dynamics. Corresponding investigations on different sizes and structures of thiolate-protected gold nanoclusters reveal their physical and chemical properties for further development of catalytic applications. In this work, we performed nonradiative relaxation dynamics simulations of the Au₃₈(SH)₂₄ nanocluster to describe electron-vibrational energy exchange. The core and higher excited states involving semiring motifs lying in the energy range of 0.00–2.01 eV are investigated using time-dependent density functional theory (TDDFT). The surface hopping method with decoherence correction combined with real-time TDDFT is used to assess the quantum dynamics. The Au₂₃ core relaxations are found to occur in the range of 2.0–8.2 ps. The higher excited states that consist of core–semiring mixed or semiring states give ultrafast decay time constants in the range of 0.6–4.9 ps. Our calculations predict that the slowest individual state decay of S₁₁ or the slowest combined S₁₁–S₁₂, S₁–S₂–S₆–S₇ and S₄–S₅–S₉–S₁₀ decay involves intracore relaxations. The analysis of the phonon spectral densities and the ground state vibrational frequencies suggests that the low frequency (25 cm^–1) coherent phonon emission reported experimentally could be the bending of the bi-icosahedral Au₂₃ core or the “fan blade twisting” mode of two icosahedral units