Perspective: Explicitly correlated electronic structure theory for complex systems Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H Today's quantum chemistry methods are extremely powerful but rely upon complex quantities such as the massively multidimensional wavefunction or even the simpler electron density. Consequently, chemical insight and a chemist's intuition are often lost in this complexity leaving the results obtained difficult to rationalize. To handle this overabundance of information, computational chemists have developed tools and methodologies that assist in composing a more intuitive picture that permits better understanding of the intricacies of chemical behavior. In particular, the fundamental comprehension of phenomena governed by non-covalent interactions is not easily achieved in terms of either the total wavefunction or the total electron density, but can be accomplished using more informative quantities. This perspective provides an overview of these tools and methods that have been specifically developed or used to analyze, identify, quantify, and visualize non-covalent interactions. These include the quantitative energy decomposition analysis schemes and the more qualitative class of approaches such as the Non-covalent Interaction index, the Density Overlap Region Indicator, or quantum theory of atoms in molecules. Aside from the enhanced knowledge gained from these schemes, their strengths, limitations, as well as a roadmap for expanding their capabilities are emphasized. ©2017Author(s).All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

Kohn-Sham density functional theory (KS-DFT) is nowadays the most widely used quantum chemical method for electronic structure calculations in chemistry and physics. Its further application in e.g. supramolecular chemistry or biochemistry has mainly been hampered by the inability of almost all current density functionals to describe the ubiquitous attractive long-range van der Waals (dispersion) interactions. We review here methods to overcome this defect, and describe in detail a very successful correction that is based on damped -C(6).R(-6) potentials (DFT-D). As examples we consider the non-covalent inter- and intra-molecular interactions in unsaturated organic molecules (so-called pi-pi stacking in benzenes and dyes), in biologically relevant systems (nucleic acid bases/pairs, proteins, and 'folding' models), between fluorinated molecules, between curved aromatics (corannulene and carbon nanotubes) and small molecules, and for the encapsulation of methane in water clusters. In selected cases we partition the interaction energies into the most relevant contributions from exchange-repulsion, electrostatics, and dispersion in order to provide qualitative insight into the binding character.

Density functional theory including dispersion corrections (DFT-D) is applied to calculate intermolecular interaction energies in an extensive benchmark set consisting mainly of DNA base pairs and amino acid pairs, for which CCSD(T) complete basis set limit estimates are available (JSCH-2005 database). The three generalized gradient approximation (GGA) density functionals B-LYP, PBE and the new B97-D are tested together with the popular hybrid functional B3-LYP. The DFT-D interaction energies deviate on average by less than 1 kcal mol(-1) or 10% from the reference values. In only six out of 161 cases, the deviation exceeds 2 kcal mol(-1). With one exception, the few larger deviations occur for non-equilibrium structures extracted from experimental geometries. The largest absolute deviations are observed for pairs of oppositely charged amino acids which are, however, not significant on a relative basis due to the huge interaction energies > 100 kcal mol(-1) involved. The counterpoise (CP) correction for the basis set superposition error with the applied triple-zeta AO basis sets varies between 0 and -1 kcal mol(-1) (<5% of the interaction energy in most cases) except for four complexes, where it is up to -1.4 kcal mol(-1). It is thus suggested to skip the laborious calculation of the CP correction in DFT-D treatments with reasonable basis sets. The three dispersion corrected GGAs considered differ mainly for the interactions of the hydrogen-bonded DNA base pairs, which are systematically too small by 0.6 kcal mol(-1) in case of B97-D, while for PBE-D they are too high by 1.5 kcal mol(-1), and for B-LYP-D by 0.5 kcal mol(-1). The all in all excellent results that have been obtained at affordable computational costs suggest the DFT-D method to be a routine tool for many applications in organic chemistry or biochemistry.

The intershell and interlayer interaction (complexation) energies of C 60 inside C 240 (C 60 @C 240 ) and of graphene sheets are investigated by all-electron density functional theory (DFT) using generalized gradient approximation (GGA) functionals and a previously developed empirical correction for dispersion (van der Waals) effects (DFT-D method). Large Gaussian basis sets of polarized triple-ζ quality that provide very small basis set superposition errors (<10% of ∆E) are employed. The theoretical approach is first applied to graphene sheet model dimers of increasing size (up to (C 216 H 36 ) 2 ). The interaction energies are extrapolated to infinite lateral size of the sheets. The value of -66 meV/atom obtained for the interaction energy of two sheets supports the most recent experimental estimate for the exfoliation energy of graphite (-52 ( 5 meV/atom). The interlayer equilibrium distance (334 ( 3 pm) is also obtained accurately. The binding energy of C 60 inside C 240 is calculated to be -184 kcal mol -1 which is about 89% of the corresponding value of a similarly sized graphene sheet model dimer. Geometric relaxation of the monomers upon complexation and nonadditivity (multilayer) effects are found to be negligible. The various contributions to the binding (Pauli exchange repulsion, electrostatic and induction, dispersion) are comparatively analyzed for the sheets and for C 60 @C 240 . The binding in both systems is that of typical van der Waals complexes; that is, the dispersion contributions play a major role as also indicated by the fact that conventional GGA functionals yield purely repulsive interactions. The plots of the electrostatic potential of the fragments often used as tools for analysis lead here to qualitatively wrong conclusions. The relatively large binding energy of C 60 @C 240 can be explained by favorable dispersion, induction, and charge-transfer interaction contributions but reveals no special role of the π orbitals. According to population analyses, about 0.67 electrons are transferred from the inner to the outer cage in C 60 @C 240 upon complex formation.

The noncovalent interactions of nucleobases and hydrogen-bonded (Watson-Crick) base-pairs on graphene are investigated with the DFT-D method, i.e., all-electron density functional theory (DFT) in generalized gradient approximation (GGA) combined with an empirical correction for dispersion (van der Waals) interactions. Full geometry optimization is performed for complexes with graphene sheet models of increasing size (up to C(150)H(30)). Large Gaussian basis sets of at least polarized triple-zeta quality are employed. The interaction energies are extrapolated to infinite lateral size of the sheets. Comparisons are made with B2PLYP-D and SCS-MP2 single point energies for coronene and C(54)H(18) substrates. The contributions to the binding (Pauli exchange repulsion, electrostatic and induction, dispersion) are analyzed. At a frozen inter-fragment distance, the interaction energy surface of the rigid C(96)H(24) and base monomers is explored in three dimensions (two lateral and one rotational). Methodologically and also regarding the results of an energy decomposition analysis, the complexes behave like other pi-stacked systems examined previously. The sequence obtained for the interaction energy of bases with graphene (G > A > T > C > U) is the same for all methods and supports recent experimental findings. The absolute values are rather large (about -20 to -25 kcal mol(-1)) but in the expected range for pi-systems of that size. The relatively short equilibrium inter-plane distance (about 3 A) is consistent with atomic force microscopy results of monolayer guanine and adenine on graphite. In graphene ... Watson-Crick pair complexes, the bases lie differently from their isolated energy minima leading to geometrical anti-cooperativity. Together with an electronic contribution of 2 and 6%, this adds up to total binding anti-cooperativities of 7 and 12% for AT and CG, respectively, on C(96)H(24). Hydrogen bonds themselves are merely affected by binding on graphene.

Photolyase is an enzyme that catalyzes photorepair of thymine dimers in UV damaged DNA by electron-transfer reaction. We docked a thymine dimer to photolyase catalytic site, using crystal structure coordinates of the substrate-free enzyme from Escherichia coli, studied molecular dynamics of the system, and calculated the electron-transfer matrix element between the lowest unoccupied molecular orbitals of flavin and the dimer. We find that the rms transfer matrix element along the dynamic trajectory is about 6 cm -1 , which is consistent with the experimentally determined rate of transfer. In the average configuration the docked thymine dimer is sitting deep in the catalytic site, and approaches the adenine of FAD with the C4dO4 carbonyl groups. The average distance between the flavin and the base pair is less than 3 Å. The electron-transfer mechanism utilizes the unusual conformation of FAD in photolyases, in which the isoalloxazine ring of the flavin and the adenine are in close proximity, and the peculiar features of the docked orientation of the dimer. The calculations show that despite the short distance between the donor and acceptor complexes, the electrontransfer mechanism between the flavin and the thymine bases is not direct, but indirect, with the adenine acting as an intermediate.

Testing of the spin-component scaled second-order Møller-Plesset (SCS-MP2) method for the computation of noncovalent interaction energies is done with a database of 165 biologically relevant complexes. The effects of the spin-scaling procedure (i.e., MP2 vs SCS-MP2), the basis set size, and the corrections for basis set superposition error (BSSE) are systematically examined. When using two-point basis set extrapolations for the correlation energy, augmentation of the atomic orbital basis with computationally costly diffuse functions is found to be obsolete. In general, SCS-MP2 also improves results for noncovalent interactions statistically on MP2, and significant outliers are removed. Moreover, it is shown that effects of BSSE and one-particle basis set incompleteness almost cancel each other in the case of triple-zeta sets (SCS-MP2/TZVPP or SCS-MP2/cc-pVTZ without counterpoise correction), which opens a practical route to efficient computations for large systems. We recommend SCS-MP2 as the preferred quantum chemical wave function based method for the noncovalent interactions in large biologically relevant systems when reasonable coupled-cluster with single and double and perturbative triple excitations (CCSD(T)) calculations cannot be performed anymore. A comparison to MP2 and CCSD(T) interaction energies for n-alkane dimers, however, indicates (and this also holds to a lesser extent for hydrogen-bonded systems) limitations of SCS-MP2 when treating chemically "saturated" interactions. The different behavior of second-order perturbation theory for saturated and for stacked pi-systems is discussed.

A recently published theoretical approach employing a nondynamic structure model using dispersion-corrected density functional theory (DFT-D3) to calculate equilibrium free energies of association (Chem. Eur. J., 2012, 18, 9955-9964) is illustrated by its application to eight new supramolecular complexes. We compare with experimentally known binding constants which span the range from -3.3 to -20.3 kcal mol(-1). The mean deviation of calculated from measured ΔGa results in 0.4 kcal mol(-1), the mean absolute deviation in 1.8 kcal mol(-1) excluding two outliers for which the computed solvation free energies are identified as the largest error source. A survey of previous applications of the theoretical approach and related computational studies is given underlining its good accuracy. It is concluded that structures and gas phase interaction energies can be computed routinely with good to high accuracy (relative errors for interaction energies of 5-10%) for complexes with about 200-300 atoms.