A density-fitting implementation of the density-based basis-set correction method.

This work reports an efficient density-fitting implementation of the density-based basis-set correction (DBBSC) method in the MOLPRO software. This method consists in correcting the energy calculated by a wave-function method with a given basis set by an adapted basis-set correction density functional incorporating the short-range electron correlation effects missing in the basis set, resulting in an accelerated convergence to the complete-basis-set limit. Different basis-set correction density-functional approximations are explored and the complementary-auxiliary-basis-set single-excitation correction is added. The method is tested on a benchmark set of reaction energies at the second-order Møller-Plesset (MP2) level and a comparison with the explicitly correlated MP2-F12 method is provided. The results show that the DBBSC method greatly accelerates the basis convergence of MP2 reaction energies, without reaching the accuracy of the MP2-F12 method but with a lower computational cost.

Thermochemical evaluation of adaptive and fixed density functional theory quadrature schemes.

A systematic study is made of the accuracy and efficiency of a number of existing quadrature schemes for molecular Kohn-Sham Density-Functional Theory (DFT) using 408 molecules and 254 chemical reactions. Included are the fixed SG-x (x = 0-3) grids of Gill et al., Dasgupta, and Herbert, the 3-zone grids of Treutler and Ahlrichs, a fixed five-zone grid implemented in Molpro, and a new adaptive grid scheme. While all methods provide a systematic reduction of errors upon extension of the grid sizes, significant differences are observed in the accuracies for similar grid sizes with various approaches. For the tests in this work, the SG-x fixed grids are less suitable to achieve high accuracies in the DFT integration, while our new adaptive grid performed best among the schemes studied in this work. The extra computational time to generate the adaptive grid scales linearly with molecular size and is negligible compared with the time needed for the self-consistent field iterations for large molecules. A comparison of the grid accuracies using various density functionals shows that meta-GGA functionals need larger integration grids than GGA functionals to reach the same degree of accuracy, confirming previous investigations of the numerical stability of meta-GGA functionals. On the other hand, the grid integration errors are almost independent of the basis set, and the basis set errors are mostly much larger than the errors caused by the numerical integrations, even when using the smallest grids tested in this work.

The Molpro quantum chemistry package.

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.

Intermolecular interaction energies from fourth order many-body perturbation theory. Impact of individual electron correlation contributions.

The performance of Møller-Plesset perturbation theory methods for describing intermolecular interaction energies has been investigated with the focus on illuminating the impact of individual electron correlation energy contributions in fourth order. It is shown that a physically meaningful decomposition of the fourth order correlation energy can be obtained by grouping individual correlation energy terms that share the same diagrammatic loop structure. This decomposition of the fourth order singles (S), doubles (D), triples (T), and quadruples (Q) terms revealed that individual terms from each excitation class can have a huge impact on the energy that is much larger than the total fourth order correlation contribution. A partial summation of S, D, and Q terms has been derived that can reproduce the full fourth order interaction energies with a good accuracy and which does not include the computationally expensive triples energy term.

Correction to: The Feynman dispersion correction for MNDO extended to F, Cl, Br and I.

A small coding error in the development version of EMPIRE led to some inconsistencies in the above article. They are corrected in this erratum.

The Feynman dispersion correction for MNDO extended to F, Cl, Br and I.

The recently introduced "Feynman" dispersion correction for MNDO (MNDO-F) has been extended to include the elements fluorine, chlorine, bromine and iodine and the original parameterization for hydrogen, carbon, nitrogen and oxygen improved by allowing individual damping radii for the elements. MNDO-F gives a root-mean-square deviation to reference interaction energies of 0.35 kcal mol-1 for the complete parameterization dataset of H, C, N, O, F, Cl, Br and I containing compounds. Graphical Abstract The electrostatic potential at the 0.001 a.u. isodensity surface of the π-complex between benzene and 1,3,5-triodobenzene calculated at the MNDO-F optimized geometry.

Study of the Wilcox torsion balance in solution for a Tröger's base derivative with hexyl-and heptyl substituents using a combined molecular mechanics and quantum chemistry approach.

The folding equilibrium of the Wilcox torsion balance in solution has been studied using a molecular mechanics method for sampling the conformational space and semi-empirical and density-functional quantum chemistry methods for characterizing the relative stabilities of various solute-solvent clusters extracted with the aid of the MD-quench technique from the different simulations that were performed. The role of the solvent environment has been analyzed by choosing four solvents of different polarities, namely water, acetone, tetrachloromethane, and n-hexane. In all cases, it is found that the attractive intramolecular interactions in folded conformations are strongly compensated by the increase of the solute-solvent interaction energies when the molecule unfolds. The latter can be well explained by the larger number of solvent molecules that can bind to the Wilcox molecule when in an unfolded conformation. The results of this work therefore support the experimental results of Yang et al. (Nature Chem 5:1006, 2013) that the folding free energy of the Wilcox balance is strongly reduced in solution as compared to the gas phase.

Geometry optimisations with a nonlocal density-functional theory method based on a double Hirshfeld partitioning.

Energy gradients have been derived for the nonlocal density-functional theory (NLDFT) method from Heßelmann [J. Chem. Theory Comput. 9, 273 (2013)]. It is shown that the derivative of the NLDFT functional can easily be obtained analytically due to the fact that the inherent Hirshfeld weights are described in terms of analytic expressions of the atomic densities determined by Slater's rules. The accuracy of the NLDFT gradient has been tested by performing geometry optimisations for a range of 76 tripeptide molecules and a number of small noncovalently bonded dimer systems for which high level coupled cluster reference structures are accessible. It was found that the resulting optimised structures are in good agreement with corresponding structures optimised using second-order Møller-Plesset or coupled cluster wave function electron correlation methods. Moreover, conformer energies as well as intermolecular interaction energies are shown to be in fair agreement with corresponding density-functional theory methods employing pairwise atom-atom dispersion models.

The coulombic σ-hole model describes bonding in CX3IY- complexes completely.

Contrary to recent reports, the σ-hole interaction energies of complexes between the carbon tetrahalides CX3I (X = F, Cl, Br, I) and halide anions Y- (Y = F, Cl, Br, I) are described very well by the simple Coulombic σ-hole concept if it is applied properly. There is no need to invoke charge transfer, which in any case is not uniquely distinguishable from polarization.

Correlation effects and many-body interactions in water clusters.

Background: The quantum-chemical description of the interactions in water clusters is an essential basis for deriving accurate and physically sound models of the interaction potential for water to be used in molecular simulations. In particular, the role of many-body interactions beyond the two-body interactions, which are often not explicitly taken into account by empirical force fields, can be accurately described by quantum chemistry methods on an adequate level, e.g., random-phase approximation electron correlation methods. The relative magnitudes of the different interaction energy contributions obtained by accurate ab initio calculations can therefore provide useful insights that can be exploited to develop enhanced force field methods. Results: In line with earlier theoretical studies of the interactions in water clusters, it has been found that the main contribution to the many-body interactions in clusters with a size of up to N = 13 molecules are higher-order polarisation interaction terms. Compared to this, many-body dispersion interactions are practically negligible for all studied sytems. The two-body dispersion interaction, however, plays a significant role in the formation of the structures of the water clusters and their stability, since it leads to a distinct compression of the cluster sizes compared to the structures optimized on an uncorrelated level. Overall, the many-body interactions amount to about 13% of the total interaction energy, irrespective of the cluster size. The electron correlation contribution to these, however, amounts to only about 30% to the total many-body interactions for the largest clusters studied and is repulsive for all structures considered in this work. Conclusion: While this shows that three- and higher-body interactions can not be neglected in the description of water complexes, the electron correlation contributions to these are much smaller in comparison to the two-body electron correlation effects. Efficient quantum chemistry approaches for describing intermolecular interactions between water molecules may therefore describe higher-body interactions on an uncorrelated Hartree-Fock level without a serious loss in accuracy.

DFT-SAPT Intermolecular Interaction Energies Employing Exact-Exchange Kohn-Sham Response Methods.

Intermolecular interaction energies have been calculated by symmetry-adapted perturbation theory based on density functional theory monomer properties (DFT-SAPT) employing response functions from time-dependent exact-exchange (TDEXX) kernels. Combined with a new asymptotic correction scheme for the exchange-correlation (xc) potentials of the monomers, which is similar in its performance to standard asymptotic correction methods, it is shown that this DFT-SAPT[TDEXX] method delivers highly accurate intermolecular interaction energies for the S22, S66, and IonHB benchmark databases by Hobza et al. A corresponding DFT-SAPT approach employing the adiabatic TDEXX kernel in the response calculations has also been tested. This DFT-SAPT[ATDEXX] method performs almost as well as DFT-SAPT[TDEXX] for dispersion-dominated dimer systems but less accurately for hydrogen-bonded dimers. Compared to this, DFT-SAPT[TDEXX] yields a balanced description of the interaction energies for various interaction-type motifs, similar to the standard DFT-SAPT method that utilizes the ALDA xc kernel to compute the response functions.

Intramolecular interactions in sterically crowded hydrocarbon molecules.

A molecular fragmentation method has been used to analyze the intramolecular interactions in the three molecules coupled diamantane, hexaphenylethane, and all-meta-tert-butyl substituted hexaphenylethane. The significance of these systems lies in the fact, that steric crowding effects enable a stabilization of the central carbon bond that possesses an extended length (1.6 to 1.7 Å) beyond conventional carbon-carbon bonds due to the steric repulsion of the attached hydrocarbon groups. The total stability of these molecules therefore depends on a delicate balance between attractive interaction forces on the one hand and on repulsive forces on the other hand. We have quantified the different interaction energy contributions using symmetry-adapted perturbation theory based on a density functional theory description of the monomers. It has been found that the attractive dispersion interactions increase more strongly with the level of crowding in the systems than the counteracting exchange interactions. This shows that steric crowding effects can have a significant impact on the structure and stability of large and branched molecules. © 2017 Wiley Periodicals, Inc.

Low scaling random-phase approximation electron correlation method including exchange interactions using localised orbitals.

A random-phase approximation electron correlation method including exchange interactions has been developed which reduces the scaling behaviour of the standard approach by two to four orders of magnitude, effectively leading to a linear scaling performance if the local structures of the underlying quantities are fully exploited in the calculations. This has been achieved by a transformation of the integrals and amplitudes from the canonical orbital basis into a local orbital basis and a subsequent dyadic screening approach. The performance of the method is demonstrated for a range of tripeptide molecules as well as for two conformers of the polyglycine molecule using up to 40 glycine units. While a reasonable agreement with the corresponding canonical method is obtained if long-range Coulomb interactions are not screened by the local method, a significant improvement in the performance is achieved for larger systems beyond 20 glycine units. Furthermore, the control of the Coulomb screening threshold allows for a quantification of intramolecular dispersion interactions, as will be exemplified for the polyglycine conformers as well as a highly branched hexaphenylethane derivate which is stabilised by steric crowding effects.

Trifluoromethyl: An Amphiphilic Noncovalent Bonding Partner.

The traditional "Fδ- " picture of fluorine suggests that it can only interact with electrophilic centers such as backbone-carbonyl carbon atoms or hydrogen-bond donors in proteins. We show that this view, which neglects polarization, is incomplete and the trifluoromethyl groups can act both as electrophiles and nucleophiles to form noncovalent interactions. The underlying polarization mechanism is based on the anomeric effect and is only fully operative if the geometry is allowed to relax. MP2/aug-cc-pVDZ calculations on model systems demonstrate the effect of the unusual group polarizability of trifluoromethyl. A survey of the Protein Databank reveals more than 600 weak interactions involving a trifluorotoluene moiety. The unique combination of the anomeric effect and the group-polarization process associated with it in CF3 allows its most negative molecular electrostatic potential (MEP) on the surface in contact with a nucleophile to become zero, so that the area of positive MEP on the backside of the carbon atom becomes dominant. However, the reverse polarization is also facile, so that CF3 can also act as an H-bond acceptor for cations such as the guanidinium group of arginine.

Accurate Intermolecular Potential for the C60 Dimer: The Performance of Different Levels of Quantum Theory.

The self-assembly of molecular building blocks is a promising route to low-cost nanoelectronic devices. It would be very appealing to use computer-aided design to identify suitable molecules. However, molecular self-assembly is guided by weak interactions, such as dispersion, which have long been notoriously difficult to describe with quantum chemical methods. In recent years, several viable techniques have emerged, ranging from empirical dispersion corrections for DFT to fast perturbation and coupled-cluster theories. In this work, we test these methods for the dimer of the prototypical building block for nanoelectronics, C60-fullerene. Benchmark quality data is obtained from DFT-based symmetry-adapted perturbation theory (SAPT), the adiabatic-connection fluctuation dissipation (ACFD) theorem using an adiabatic LDA kernel, and domain-based local pair natural orbital (DLPNO) coupled-pair and coupled-cluster methods. These benchmarks are used to evaluate economical dispersion-corrected DFT methods, double-hybrid DFT functionals, and second-order Møller-Plesset theory. Furthermore, we provide analytical fits to the benchmark interaction curves, which can be used for a coarse-grain description of fullerene self-assembly. These analytical expressions differ significantly from those reported previously based on bulk data.

On the Stability of Cyclophane Derivates Using a Molecular Fragmentation Method.

A molecular fragmentation method is used to study the stability of cyclophane derivates by decomposing the molecular energy into the molecular strain and intramolecular interaction energies. The molecular strain energies obtained by utilising the fragmentation method are in good agreement with existing experimental data. The intramolecular interaction energies calculated as the difference between the supermolecular energy and the bonded fragment energies are repulsive in the cyclophanes studied. The nature of this interaction is studied for groups of systematically extended doubled layered paracyclophane systems using the random-phase approximation (RPA), two recently developed extensions to the RPA and standard density functional theory (DFT) methods including dispersion corrections. Upon a systematic increase in conjugation the strongly repulsive intramolecular interaction energy reduces and thus leads to an increase in the stability. Finally, existing experimental and theoretical estimates of the molecular strain are compared with the results of this work.

Local Molecular Orbitals from a Projection onto Localized Centers.

A localization method for molecular orbitals is presented which exploits the locality of the eigenfunctions associated with the largest eigenvalues of the matrix representation of spatially localized functions. Local molecular orbitals are obtained by a projection of the canonical orbitals onto the set of the eigenvectors which correspond to the largest eigenvalues of these matrices. Two different types of spatially localized functions were chosen in this work, a two-parameter smooth-step-type function and the weight functions determined by a Hirshfeld partitioning of the molecular volume. It is shown that the method can provide fairly local occupied molecular orbitals if the positions of the set of local functions are set to the molecular bond centers. The method can also yield reasonably well-localized virtual molecular orbitals, but here, a sensible choice of the positions of the functions are the atomic sites and the locality then depends more strongly on the shape of the set of local functions. The method is tested for a range of polypeptide molecules in two different conformations, namely, a helical and a ß-sheet conformation. Futhermore, it is shown that an adequate locality of the occupied and virtual orbitals can also be obtained for highly delocalized systems.

Molecular energies from an incremental fragmentation method.

The systematic molecular fragmentation method by Collins and Deev [J. Chem. Phys. 125, 104104 (2006)] has been used to calculate total energies and relative conformational energies for a number of small and extended molecular systems. In contrast to the original approach by Collins, we have tested the accuracy of the fragmentation method by utilising an incremental scheme in which the energies at the lowest level of the fragmentation are calculated on an accurate quantum chemistry level while lower-cost methods are used to correct the low-level energies through a high-level fragmentation. In this work, the fragment energies at the lowest level of fragmentation were calculated using the random-phase approximation (RPA) and two recently developed extensions to the RPA while the incremental corrections at higher levels of the fragmentation were calculated using standard density functional theory (DFT) methods. The complete incremental fragmentation method has been shown to reproduce the supermolecule results with a very good accuracy, almost independent on the molecular type, size, or type of decomposition. The fragmentation method has also been used in conjunction with the DFT-SAPT (symmetry-adapted perturbation theory) method which enables a breakdown of the total nonbonding energy contributions into individual interaction energy terms. Finally, the potential problems of the method connected with the use of capping hydrogen atoms are analysed and two possible solutions are supplied.

Molecular Excitation Energies from Time-Dependent Density Functional Theory Employing Random-Phase Approximation Hessians with Exact Exchange.

Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.

Polarisabilities of long conjugated chain molecules with density functional response methods: The role of coupled and uncoupled response.

The longitudinal component of the dipole-dipole polarisability of polyacetylene molecules containing 4 to 20 carbon atoms has been calculated with density-functional theory (DFT) response methods. In order to analyse the effect of the uncoupled and coupled contributions to the response matrix, a number of different sets of orbitals were combined with different approximations for the Hessian matrix. This revealed a surprising result: a qualitatively correct increase of the polarisability with the chain length can already be reproduced on the uncoupled level if the response matrix is constructed from Hartree-Fock (HF) or exact-exchange (EXX) DFT orbitals. The nonlocal HF and the local EXX exchange potentials both produce a displacement of charge from the chain ends to the centre of the polyacetylene molecule compared to DFT methods using standard exchange-correlation potentials. In this way, the reduced increase of the transition dipole moments along the molecular axis counteracts the decrease of the occupied-virtual orbital energy gaps and leads to a linear dependence of the polarisabilities (normalised by the number of carbon atoms) on the chain length. A new DFT response approach is tested which utilises unitary transformed Hartree-Fock orbitals as input and which resolves the failure of standard DFT response methods.