A quantum chemical method based on a Hartree-Fock calculation with a small Gaussian AO basis set is presented. Its main area of application is the computation of structures, vibrational frequencies, and noncovalent interaction energies in huge molecular systems. The method is suggested as a partial replacement of semiempirical approaches or density functional theory (DFT) in particular when self-interaction errors are acute. In order to get accurate results three physically plausible atom pair-wise correction terms are applied for London dispersion interactions (D3 scheme), basis set superposition error (gCP scheme), and short-ranged basis set incompleteness effects. In total nine global empirical parameters are used. This so-called Hartee-Fock-3c (HF-3c) method is tested for geometries of small organic molecules, interaction energies and geometries of noncovalently bound complexes, for supramolecular systems, and protein structures. In the majority of realistic test cases good results approaching large basis set DFT quality are obtained at a tiny fraction of computational cost.

The S12L test set for supramolecular Gibbs free energies of association ΔGa (Grimme, S. Chem. Eur. J. 2012, 18, 9955-9964) is extended to 30 complexes (S30L), featuring more diverse interaction motifs, anions, and higher charges (-1 up to +4) as well as larger systems with up to 200 atoms. Various typical noncovalent interactions like hydrogen and halogen bonding, π-π stacking, nonpolar dispersion, and CH-π and cation-dipolar interactions are represented by "real" complexes. The experimental Gibbs free energies of association (ΔGa exp) cover a wide range from -0.7 to -24.7 kcal mol-1. In order to obtain a theoretical best estimate for ΔGa, we test various dispersion corrected density functionals in combination with quadruple-ζ basis sets for calculating the association energies in the gas phase. Further, modern semiempirical methods are employed to obtain the thermostatistical corrections from energy to Gibbs free energy, and the COSMO-RS model with several parametrizations as well as the SMD model are used to include solvation contributions. We investigate the effect of including counterions for the charged systems (S30L-CI), which is found to overall improve the results. Our best method combination consists of PW6B95-D3 (for neutral and charged systems) or ωB97X-D3 (for systems with counterions) energies, HF-3c thermostatistical corrections, and Gibbs free energies of solvation obtained with the COSMO-RS 2012 parameters for nonpolar solvents and 2013-fine for water. This combination gives a mean absolute deviation for ΔGa of only 2.4 kcal mol-1 (S30L) and 2.1 kcal mol-1 (S30L-CI), with a mean deviation of almost zero compared to experiment. Regarding the relative Gibbs free energies of association for the 13 pairs of complexes which share the same host, the correct trend in binding affinities could be reproduced except for two cases. The MAD compared to experiment amounts to 1.2 kcal mol-1, and the MD is almost zero. The best-estimate theoretical corrections are used to back-correct the experimental ΔGa values in order to get an empirical estimate for the "experimental", zero-point vibrational energy exclusive, gas phase binding energies. These are then utilized to benchmark the performance of various "lowcost" quantum chemical methods for noncovalent interactions in large systems. The performance of other common DFT methods as well as the use of semiempirical methods for structure optimizations is discussed.

Quantum chemical calculations using DFT (BP86, M05-2X) and ab initio methods (CCSD(T), SCS-MP2) have been carried out on the borylene complexes (BH)L(2) and nitrogen cation complexes (N(+))L(2) with the ligands L=CO, N(2), PPh(3), NHC(Me), CAAC, and CAAC(model). The results are compared with those obtained for the isoelectronic carbones CL(2). The geometries and bond dissociation energies of the ligands, the proton affinities, and adducts with the Lewis acids BH(3) and AuCl were calculated. The nature of the bonding has been analyzed with charge and energy partitioning methods. The calculated borylene complexes (BH)L(2) have trigonal planar coordinated boron atoms which possess rather short B-L bonds. The calculated bond dissociation energies (BDEs) of the ligands for complexes where L is a carbene (NHC or CAAC) are very large (D(e) =141.6-177.3 kcal mol(-1)) which suggest that such species might become isolated in a condensed phase. The borylene complexes (BH)(PPh(3))(2) and (BH)(CO)(2) have intermediate bond strengths (D(e) =90.1 and 92.6 kcal mol(-1)). Substituted homologues with bulky groups at boron which protect the boron atom from electrophilic attack might also be stable enough to become isolated. The BDE of (BH)(N(2))(2) is much smaller (D(e) =31.9 kcal mol(-1)), but could become observable in a low-temperature matrix. The proton affinities of the borylene complexes are very large, particularly for the bulky adducts with L=PPh(3), NHC(Me), CAAC(model) and CAAC and thus, they are superbases. All (BH)L(2) molecules bind strongly AuCl either η(1) (L=N(2), PPh(3), NHC(Me), CAAC) or η(2) (L=CO, CAAC(model)). The BDEs of H(3)B-(BH)L(2) adducts which possess a hitherto unknown boron→boron donor-acceptor bond are smaller than for the AuCl complexes. The strongest bonded BH(3) adduct that might be isolable is (BH)(PPh(3))(2)-BH(3) (D(e) =36.2 kcal mol(-1)). The analysis of the bonding situation reveals that (BH)-L(2) bonding comes mainly from the orbital interactions which has three major contributions, that is, the donation from the symmetric (σ) and antisymmetric (π(||)) combination of the ligand lone-pair orbitals into the vacant MOs of BH L→(BH)←L and the L←(BH)→L π backdonation from the boron lone-pair orbital. The nitrogen cation complexes (N(+))L(2) have strongly bent L-N-L geometries, in which the calculated bending angle varies between 113.9° (L=N(2)) and 146.9° (L=CAAC). The BDEs for (N(+))L(2) are much larger than those of the borylene complexes. The carbene ligands NHC and CAAC but also the phosphane ligands PPh(3) bind very strongly between D(e) =358.4 kcal mol(-1) (L=PPh(3)) and D(e) =412.5 kcal mol(-1) (L=CAAC(model)). The proton affinities (PA) of (N(+))L(2) are much smaller and they bind AuCl and BH(3) less strongly compared with (BH)L(2). However, the PAs (N(+))L(2) for complexes with bulky ligands L are still between 139.9 kcal mol(-1) (L=CAAC(model)) and 168.5 kcal mol(-1) (L=CAAC). The analysis of the (N(+))-L(2) bonding situation reveals that the binding interactions come mainly from the L→(...

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.