We evaluate the performance of the most widely used wavefunction, density functional theory, and semiempirical methods for the description of noncovalent interactions in a set of larger, mostly dispersion-stabilized noncovalent complexes (the L7 data set). The methods tested include MP2, MP3, SCS-MP2, SCS(MI)-MP2, MP2.5, MP2.X, MP2C, DFT-D, DFT-D3 (B3-LYP-D3, B-LYP-D3, TPSS-D3, PW6B95-D3, M06-2X-D3) and M06-2X, and semiempirical methods augmented with dispersion and hydrogen bonding corrections: SCC-DFTB-D, PM6-D, PM6-DH2 and PM6-D3H4. The test complexes are the octadecane dimer, the guanine trimer, the circumcoronene…adenine dimer, the coronene dimer, the guanine-cytosine dimer, the circumcoronene…guanine-cytosine dimer, and an amyloid fragment trimer containing phenylalanine residues. The best performing method is MP2.5 with relative root mean square deviation (rRMSD) of 4 %. It can thus be recommended as an alternative to the CCSD(T)/CBS (alternatively QCISD(T)/CBS) benchmark for molecular systems which exceed current computational capacity. The second best non-DFT method is MP2C with rRMSD of 8 %. A method with the most favorable “accuracy/cost” ratio belongs to the DFT family: BLYP-D3, with an rRMSD of 8 %. Semiempirical methods deliver less accurate results (the rRMSD exceeds 25 %). Nevertheless, their absolute errors are close to some much more expensive methods such as M06-2X, MP2 or SCS(MI)-MP2, and thus their price/performance ratio is excellent.

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The efficient and accurate description of the electronic structure of strongly correlated systems is still a largely unsolved problem. The usual procedures start with a multiconfigurational (usually a Complete Active Space, CAS) wavefunction which accounts for static correlation and add dynamical correlation by perturbation theory, configuration interaction, or coupled cluster expansion. This procedure requires the correct selection of the active space. Intuitive methods are unreliable for complex systems. The inexpensive black-box unrestricted natural orbital (UNO) criterion postulates that the Unrestricted Hartree-Fock (UHF) charge natural orbitals with fractional occupancy (e.g., between 0.02 and 1.98) constitute the active space. UNOs generally approximate the CAS orbitals so well that the orbital optimization in CAS Self-Consistent Field (CASSCF) may be omitted, resulting in the inexpensive UNO-CAS method. A rigorous testing of the UNO criterion requires comparison with approximate full configuration interaction wavefunctions. This became feasible with the advent of Density Matrix Renormalization Group (DMRG) methods which can approximate highly correlated wavefunctions at affordable cost. We have compared active orbital occupancies in UNO-CAS and CASSCF calculations with DMRG in a number of strongly correlated molecules: compounds of electronegative atoms (F2, ozone, and NO2), polyenes, aromatic molecules (naphthalene, azulene, anthracene, and nitrobenzene), radicals (phenoxy and benzyl), diradicals (o-, m-, and p-benzyne), and transition metal compounds (nickel-acetylene and Cr2). The UNO criterion works well in these cases. Other symmetry breaking solutions, with the possible exception of spatial symmetry, do not appear to be essential to generate the correct active space. In the case of multiple UHF solutions, the natural orbitals of the average UHF density should be used. The problems of the UNO criterion and their potential solutions are discussed: finding the UHF solutions, discontinuities on potential energy surfaces, and inclusion of dynamical electron correlation and generalization to excited states.

Stacking interaction between π systems is a well recognized structural motif but stacking between σ systems was long considered of secondary importance. A recent paper points out that σ stacking can reach the energy of chemical bonds, and concludes that “σ/σ and π/π interactions are equally important” (Fokin, A. F.; Gerbig, D.; Schreiner, P. R., J. Am. Chem. Soc. 2011, 133, 20036). Our analysis shows that strong dispersion interaction requires rigid subsystems and a good fit of their repulsive potential walls, satisfied for both graphenes and larger graphanes (perhydrographenes). Comparison of the dimerization energies of decalin and perhydrocoronene with the naphthalene and coronene dimers at the Coupled Cluster (CC) CCSD(T) level confirms the substantial σ stacking energies in graphanes but gives lower binding energies than the B97D calculations of Fokin et al. Graphane dimerization energies are substantially lower at the CC level than the corresponding π stacking energies: the value for perhydrocoronene is only 67 % of the value for coronene, and the difference increases with system size. Our best estimate for the dimerization energy of naphthalene is 6.1 kcal/mol. Spin component scaled MP2 is unbalanced: it gives only 70 % of the CCSD(T) binding energy in σ dimers. The B3LYP D3 method compares very well with CC for both σ and π dimers at the van der Waals minimum but underestimates the binding at larger distances. We used the largest possible atomic basis for these systems with 64 bit arithmetic, half augmented pVDZ, and the results were corrected for basis set incompleteness at the MP2 level.

This article describes the capabilities and performance of the latest release (version 4.0) of the Parallel Quantum Solutions (PQS) ab initio program package. The program was first released in 1998 and evolved from the TEXAS program package developed by Pulay and coworkers in the late 1970s. PQS was designed from the start to run on Linux-based clusters (which at the time were just becoming popular) with all major functionality being (a) fully parallel; and (b) capable of carrying out calculations on large-by ab initio standards-molecules, our initial aim being at least 100 atoms and 1000 basis functions with only modest memory requirements. With modern hardware and recent algorithmic developments, full accuracy, high-level calculations (DFT, MP2, CI, and Coupled-Cluster) can be performed on systems with up to several thousand basis functions on small (4-32 node) Linux clusters. We have also developed a graphical user interface with a model builder, job input preparation, parallel job submission, and post-job visualization and display.