We present a detailed analysis of several time-dependent DFT (TD-DFT) methods, including conventional hybrid functionals and two types of nonempirically tuned range-separated functionals, for predicting a diverse set of electronic excitations in DNA nucleobase monomers and dimers. This large and extensive set of excitations comprises a total of 50 different transitions (for each tested DFT functional) that includes several n → π and π → π* valence excitations, long-range charge-transfer excitations, and extended Rydberg transitions (complete with benchmark calculations from high-level EOM-CCSD(T) methods). The presence of localized valence excitations as well as extreme long-range charge-transfer excitations in these systems poses a serious challenge for TD-DFT methods that allows us to assess the importance of both short- and long-range exchange contributions for simultaneously predicting all of these various transitions. In particular, we find that functionals that do not have both short- and full long-range exchange components are unable to predict the different types of nucleobase excitations with the same accuracy. Most importantly, the current study highlights the importance of both short-range exchange and a nonempirically tuned contribution of long-range exchange for accurately predicting the diverse excitations in these challenging nucleobase systems.

We present a new analysis of exchange and dispersion effects for calculating halogen-bonding interactions in a wide variety of complex dimers (69 total) within the XB18 and XB51 benchmark sets. Contrary to previous work on these systems, we find that dispersion plays a more significant role than exact exchange in accurately calculating halogen-bonding interaction energies, which are further confirmed by extensive SAPT analyses. In particular, we find that even if the amount of exact exchange is nonempirically tuned to satisfy known DFT constraints, we still observe an overall improvement in predicting dissociation energies when dispersion corrections are applied, in stark contrast to previous studies ( Kozuch, S.; Martin, J. M. L. J. Chem. Theory Comput. 2013 , 9 , 1918 - 1931 ). In addition to these new analyses, we correct several (14) inconsistencies in the XB51 set, which is widely used in the scientific literature for developing and benchmarking various DFT methods. Together, these new analyses and revised benchmarks emphasize the importance of dispersion and provide corrected reference values that are essential for developing/parametrizing new DFT functionals, specifically for complex halogen-bonding interactions.

Conformational ensembles of individual amino acid residues within model GxG peptides (x representing different amino acid residues) are dominated by a mixture of polyproline II (pPII) and β-strand like conformations. We recently discovered rather substantial differences between the enthalpic and entropic contributions to this equilibrium for different amino acid residues. Isoleucine and valine exceed all other amino acid residues in terms of their rather large enthalpic stabilization and entropic destabilization of polyproline II. In order to shed light on these underlying physical mechanisms, we performed high-level DFT calculations to explore the energetics of four representative GxG peptides where x = alanine (A), leucine (L), valine (V), and isoleucine (I) in explicit water (10 H2O molecules with a polarizable continuum water model) and in vacuo. We found that the large energetic contributions to the stabilization of pPII result, to a major extent, from peptide-water, water-water interactions, and changes of the solvent self-energy. Differences between the peptide-solvent interaction energies of hydration in pPII and β-strand peptides are particularly important for the pPII ⇌ β equilibria of the more aliphatic peptides GIG and GLG. Furthermore, we performed a vibrational analysis of the four peptides in both conformations and discovered a rather substantial mixing between water motions and peptide vibrations below 700 cm(-1). We found that the respective vibrational entropies are substantially different for the considered conformations, and their contributions to the Gibbs/Helmholtz energy stabilize β-strand conformations. Taken together, our results underscore the notion of the solvent being the predominant determinant of peptide (and protein) conformations in the unfolded state.

A ring-shaped carbon allotrope was recently synthesized for the first time, reinvigorating theoretical interest in this class of molecules.

Off-diagonal long-range order (ODLRO) in the two-electron reduced density matrix (2-RDM) has long been recognized as a mathematical characteristic of conventional superconductors. The large eigenvalue of the 2-RDM has been shown to be a useful measure of this long-range order. The 2-RDM can be represented as a sum of a connected (cumulant) and unconnected piece. In this work, we show that the cumulant 2-RDM also has a large eigenvalue in the limit of ODLRO. The largest eigenvalue of the cumulant 2-RDM, we prove, is bounded from above by N. In the limit of extreme pairing, such as Cooper pairing, the largest eigenvalue and the trace of the cumulant 2-RDM approach their extreme values of N and −N , respectively. While the trace of the cumulant 2-RDM, which is computable from only a knowledge of the 1-RDM, can reflect ODLRO, it alone does not appear to be a sufficient criterion. The large eigenvalue of the cumulant 2-RDM, we show, implies the large eigenvalue of the 2-RDM, and hence, is a natural measure of ODLRO that vanishes in the mean-field limit.