Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

The symmetry-adapted perturbation theory (SAPT) has been employed to calculate an accurate potential energy curve for the helium dimer. For major components of the interaction energy, saturated values have been obtained using extended Gaussian-type geminal bases. Some other, less significant components were computed using a large orbital basis and the standard set of SAPT codes. The remaining small fraction of the interaction energy has been obtained using a nonstandard SAPT program specific for two-electron monomers and the supermolecular full configuration interaction (FCI) calculations in a moderately large orbital basis. Accuracy of the interaction energy components has been carefully examined. The most accurate to date values of the electrostatic, exchange, induction, and dispersion energies are reported for distances from 3.0 to 7.0 bohr. After adding the retardation correction predicted by the Casimir theory, our new potential has been shown [A. R. Janzen and R. A. Aziz (submitted)] to recover the known bulk and scattering data for helium more accurately than other existing ab initio and empirical potentials. However, the calculated dissociation energy of 1.713 mK and the bond length of 45.8 Å differ somewhat from the values inferred recently from a transmission experiment using nanoscale sieves.

The Equation-of-Motion coupled cluster method restricted to single and double excitations (EOM-CCSD) and singlet excited states is formulated in a basis of nonorthogonal local orbitals. In the calculation of excited states only electron promotions from localized molecular orbitals into subspaces (excitation domains) of the local basis are allowed, which strongly reduces the number of EOM-CCSD amplitudes to be optimized. Furthermore, double excitations are neglected unless the excitation domains of the corresponding localized occupied orbitals are close to each other. Unlike in the local methods for the ground state, the excitation domains cannot be simply restricted to the atomic orbitals that are spatially close to the localized occupied orbitals. In the present paper the choice of the excitation domains is based on the analysis of wave functions computed by more approximate (and cheaper) methods like, e.g., configuration-interaction singles. The effect of various local approximations is investigated in detail, and it is found that a balanced description of the local configuration spaces describing the ground and excited states is essential to obtain accurate results. Using a single set of parameters for a given basis set, test calculations with the local EOM-CCSD method were performed for 14 molecules and 49 electronically excited states. The excitation energies computed by the local EOM-CCSD method reproduce the conventional EOM-CCSD excitation energies with an average error of 0.06 eV.

A new local method for the computation of electronic excitation energies of singlet states in extended molecular systems is presented. It is based on the CC2 model and local approximations to the wave functions. In the proposed method the singles excitations are treated nonlocally and local restrictions are imposed on doubles amplitudes only. The accuracy of the new method was tested by calculating several lowest excited states for 14 molecules and comparing them with canonical CC2 values. Deviations of the local excitation energies from the canonical reference values do not exceed 0.05 eV for all test molecules and all states in the lower energy range investigated in this work. The method uses the density-fitting approximation for all two-electron integrals, which considerably simplifies the computational complexity of the individual diagrams. A combination of the local approximations and the powerful density-fitting technique leads to a low-scaling method, capable to treat molecular systems comprised of 100 atoms and more in a basis of a polarized double zeta quality. A test calculation for a system consisting of 127 atoms and 370 active electrons without symmetry is presented to show the efficiency of the new method.

Binding energies for the complexes of the S12L database by Grimme [Chem. Eur. J. 18, 9955 (2012)] were calculated using intermolecular symmetry-adapted perturbation theory combined with a density-functional theory description of the interacting molecules. The individual interaction energy decompositions revealed no particular change in the stabilisation pattern as compared to smaller dimer systems at equilibrium structures. This demonstrates that, to some extent, the qualitative description of the interaction of small dimer systems may be extrapolated to larger systems, a method that is widely used in force-fields in which the total interaction energy is decomposed into atom-atom contributions. A comparison of the binding energies with accurate experimental reference values from Grimme, the latter including thermodynamic corrections from semiempirical calculations, has shown a fairly good agreement to within the error range of the reference binding energies.

Because of difficulties in a description of host-guest interactions, various theoretical methods predict different numbers of hydrogen molecules which can be inserted into the C60 cavity, ranging from one to more than 20. On the other hand, only one H2 molecule inside the C60 fullerene has been detected experimentally. Moreover, a recently synthesized H2@C70 complex prevails in the mixture formed with 2H2@C70. To get a deeper insight into the stability of the complexes created from C60 and hydrogen molecules, we carried out highly accurate calculations for complexes of one or two hydrogen molecules with fullerene applying symmetry-adapted perturbation theory (SAPT) and a large TZVPP basis set for selected points on the potential energy surfaces of H2@C60 and 2H2@C60. The electron correlation in the host and guests has been treated by density functional theory. Our calculations yield the stability of the recently synthesized H2@C60 complex. In addition, for all tried positions of the H2 dimer inside the C60 cage, the 2H2@C60 complex has been characterized by a positive interaction energy corresponding to the instability of this species. Contrary to the conclusions of several theoretical studies, this finding, as well as model considerations and literature experimental data, indicates that only one hydrogen molecule can reside inside the C60 cage. The calculated energy components have been analyzed to identify the most important contributions to the interaction energy. Supermolecular interaction energies obtained with MP2, SCS-MP2, and DFT+Disp methods are also reported and compared to those of DFT-SAPT. The DFT-SAPT interaction energy has also been calculated for several points on the potential energy surface for a larger 2H2@C70 complex, confirming, in agreement with recent experimental findings, that this species is stable. The DFT-SAPT approach has been used for the first time to obtain interaction energies for van der Waals endohedral complexes, demonstrating that the method is capable of handling such difficult cases.

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Selected points on the potential energy surface for the complexes Rg@C(60) (Rg = He, Ne, Ar, Kr) are calculated with various theoretical methods, like symmetry-adapted perturbation theory with monomers described by density functional theory (DFT-SAPT), supermolecular Møller-Plesset theory truncated on the second order (MP2), spin-component-scaled MP2 (SCS-MP2), supermolecular density functional theory with empirical dispersion correction (DFT+Disp), and the recently developed MP2C method that improves the MP2 method for long-range electron correlation effects. A stabilization of the endohedral complex is predicted by all methods, but the depth of the potential energy well is overestimated by the DFT+Disp and MP2 approaches. On the other hand, the MP2C model agrees well with DFT-SAPT, which serves as the reference. The performance of SCS-MP2 is mixed: it produces too low interaction energies for the two heavier guests, while its accuracy for He@C(60) and Ne@C(60) is similar to that of MP2C. Fitting formulas for the main interaction energy components, i.e. the dispersion and first-order repulsion energies are proposed, which are applicable for both endo- and exohedral cases. For all examined methods density fitting is used to evaluate two-electron repulsion integrals, which is indispensable to allow studies of noncovalent complexes of this size. It has been found that density-fitting auxiliary basis sets cannot be used in a black-box fashion for the calculation of the first-order SAPT electrostatic energy, and that the quality of these basis sets should be always carefully examined in order to avoid an unphysical long-range behavior.