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A study is conducted to examine H(sub 2)S-benzene dimer as the simplest model of sulfur-Pi interactions. Analysis of the interaction using symmetry-adapted perturbation theory, along with potential energy curve for rotation of the H(sub 2)S unit relative to the benzene ring, suggests that the sulfur-Pi interaction is an electrostatic attraction between the partial positive hydrogen in H(sub 2)S and the negatively charged Pi electrons of benzene.

The sandwich and T-shaped configurations of benzene dimers are investigated to elucidate how substituents tune Pi-Pi interactions. All substituted sandwich dimers bind more strongly than benzene dimer.

Symmetry-Adapted Perturbation Theory (SAPT) is one of the most popular approaches to energy component analysis of non-covalent interactions between closed-shell systems, yielding both accurate interaction energies and meaningful interaction energy components. In recent years, the full open-shell equations for SAPT up to second-order in the intermolecular interaction and zeroth-order in the intramolecular correlation (SAPT0) were published [P. S. Zuchowski et al., J. Chem. Phys. 129, 084101 (2008); M. Hapka et al., ibid. 137, 164104 (2012)]. Here, we utilize density-fitted electron repulsion integrals to produce an efficient computational implementation. This approach is used to examine the effect of ionization on π-π interactions. For the benzene dimer radical cation, comparison against reference values indicates a good performance for open-shell SAPT0, except in cases with substantial charge transfer. For π stacking between hydrogen-bonded pairs of nucleobases, dispersion interactions still dominate binding, in spite of the creation of a positive charge. [ABSTRACT FROM AUTHOR]

An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the "gradient terms": computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C10H22), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies. [ABSTRACT FROM AUTHOR]

The title electronic states of the nitrenium ion have been investigated by ab initio molecular electronic structure calculations. The equilibrium geometries, harmonic vibrational frequencies, infrared intensities and dipole moments were determined by self-consistent-field, configuration interaction with single and double excitations and complete active space wave functions. The results showed that the ground, first and second excited states are bent while the third excite state is linear in geometries.

Ab initio electronic structure procedures were employed in investigating the lowest singlet and triplet states of cyclopropyne and silacyclopropyne. Restricted Hartree-Fock or self-consistent-field, two-configuration self-consistent-field, single and double excitation configuration interaction and coupled cluster (CCSD), and CCSD incorporating perturbative estimates of connected triple excitations were used to derive optimum geometries and harmonic vibrational frequencies.

We develop a simple methodology for the computation of symmetry-adapted perturbation theory (SAPT) interaction energy contributions for intramolecular noncovalent interactions. In this approach, the local occupied orbitals of the total Hartree-Fock (HF) wavefunction are used to partition the fully interacting system into three chemically identifiable units: the noncovalent fragments A and B and a covalent linker C. Once these units are identified, the noninteracting HF wavefunctions of the fragments A and B are separately optimized while embedded in the HF wavefunction of C, providing the dressed zeroth order wavefunctions for A and B in the presence of C. Standard two-body SAPT (particularly SAPT0) is then applied between the relaxed wavefunctions for A and B. This intramolecular SAPT procedure is found to be remarkably straightforward and efficient, as evidenced by example applications ranging from diols to hexaphenyl-ethane derivatives. [ABSTRACT FROM AUTHOR]

A systematic examination of noncovalent interactions as modeled by wavefunction theory is presented in comparison to gold-standard quality benchmarks available for 345 interaction energies of 49 bimolecular complexes. Quantum chemical techniques examined include spin-component-scaling (SCS) variations on second-order perturbation theory (MP2) [SCS, SCS(N), SCS(MI)] and coupled cluster singles and doubles (CCSD) [SCS, SCS(MI)]; also, method combinations designed to improve dispersion contacts [DW-MP2, MP2C, MP2.5, DW-CCSD(T)-F12]; where available, explicitly correlated (F12) counterparts are also considered. Dunning basis sets augmented by diffuse functions are employed for all accessible Z-levels; truncations of the diffuse space are also considered. After examination of both accuracy and performance for 394 model chemistries, SCS(MI)-MP2/cc-pVQZ can be recommended for general use, having good accuracy at low cost and no ill-effects such as imbalance between hydrogen-bonding and dispersion-dominated systems or non-parallelity across dissociation curves. Moreover, when benchmarking accuracy is desirable but gold-standard computations are unaffordable, this work recommends silver-standard [DW-CCSD(T**)-F12/aug-cc-pVDZ] and bronze-standard [MP2C-F12/aug-cc-pVDZ] model chemistries, which support accuracies of 0.05 and 0.16 kcal/mol and efficiencies of 97.3 and 5.5 h for adenine · thymine, respectively. Choice comparisons of wavefunction results with the best symmetry-adapted perturbation theory [T. M. Parker, L. A. Burns, R. M. Parrish, A. G. Ryno, and C. D. Sherrill, J. Chem. Phys. 140, 094106 (2014)] and density functional theory [L. A. Burns, Á. Vázquez-Mayagoitia, B. G. Sumpter, and C. D. Sherrill, J. Chem. Phys. 134, 084107 (2011)] methods previously studied for these databases are provided for readers' guidance. [ABSTRACT FROM AUTHOR]

Orbital-optimized MP2.5 [or simply "optimized MP2.5," OMP2.5, for short] and its analytic energy gradients are presented. The cost of the presented method is as much as that of coupled-cluster singles and doubles (CCSD) [O(N6) scaling] for energy computations. However, for analytic gradient computations the OMP2.5 method is only half as expensive as CCSD because there is no need to solve λ2-amplitude equations for OMP2.5. The performance of the OMP2.5 method is compared with that of the standard second-order Møller-Plesset perturbation theory (MP2), MP2.5, CCSD, and coupled-cluster singles and doubles with perturbative triples (CCSD(T)) methods for equilibrium geometries, hydrogen transfer reactions between radicals, and noncovalent interactions. For bond lengths of both closed and open-shell molecules, the OMP2.5 method improves upon MP2.5 and CCSD by 38%-43% and 31%-28%, respectively, with Dunning's cc-pCVQZ basis set. For complete basis set (CBS) predictions of hydrogen transfer reaction energies, the OMP2.5 method exhibits a substantially better performance than MP2.5, providing a mean absolute error of 1.1 kcal mol-1, which is more than 10 times lower than that of MP2.5 (11.8 kcal mol-1), and comparing to MP2 (14.6 kcal mol-1) there is a more than 12-fold reduction in errors. For noncovalent interaction energies (at CBS limits), the OMP2.5 method maintains the very good performance of MP2.5 for closed-shell systems, and for open-shell systems it significantly outperforms MP2.5 and CCSD, and approaches CCSD(T) quality. The MP2.5 errors decrease by a factor of 5 when the optimized orbitals are used for open-shell noncovalent interactions, and comparing to CCSD there is a more than 3-fold reduction in errors. Overall, the present application results indicate that the OMP2.5 method is very promising for open-shell noncovalent interactions and other chemical systems with difficult electronic structures. [ABSTRACT FROM AUTHOR]

We develop a physically-motivated assignment of symmetry adapted perturbation theory for intermolecular interactions (SAPT) into atom-pairwise contributions (the A-SAPT partition). The basic precept of A-SAPT is that the many-body interaction energy components are computed normally under the formalism of SAPT, following which a spatially-localized two-body quasiparticle interaction is extracted from the many-body interaction terms. For electrostatics and induction source terms, the relevant quasiparticles are atoms, which are obtained in this work through the iterative stockholder analysis (ISA) procedure. For the exchange, induction response, and dispersion terms, the relevant quasiparticles are local occupied orbitals, which are obtained in this work through the Pipek-Mezey procedure. The local orbital atomic charges obtained from ISA additionally allow the terms involving local orbitals to be assigned in an atom-pairwise manner. Further summation over the atoms of one or the other monomer allows for a chemically intuitive visualization of the contribution of each atom and interaction component to the overall noncovalent interaction strength. Herein, we present the intuitive development and mathematical form for A-SAPT applied in the SAPT0 approximation (the A-SAPT0 partition). We also provide an efficient series of algorithms for the computation of the A-SAPT0 partition with essentially the same computational cost as the corresponding SAPT0 decomposition. We probe the sensitivity of the A-SAPT0 partition to the ISA grid and convergence parameter, orbital localization metric, and induction coupling treatment, and recommend a set of practical choices which closes the definition of the A-SAPT0 partition. We demonstrate the utility and computational tractability of the A-SAPT0 partition in the context of side-on cation-p interactions and the intercalation of DNA by proflavine. A-SAPT0 clearly shows the key processes in these complicated noncovalent interactions, in systems with up to 220 atoms and 2845 basis functions. [ABSTRACT FROM AUTHOR]

Coupled-cluster theory including single, double, and perturbative triple excitations [CCSD(T)] has been applied to trimers that appear in crystalline benzene in order to resolve discrepancies in the literature about the magnitude of non-additive three-body contributions to the lattice energy. The present results indicate a non-additive three-body contribution of 0.89 kcal mol-1, or 7.2% of the revised lattice energy of -12.3 kcal mol-1. For the trimers for which we were able to compute CCSD(T) energies, we obtain a sizeable difference of 0.63 kcal mol-1 between the CCSD(T) and MP2 three-body contributions to the lattice energy, confirming that three-body dispersion dominates over three-body induction. Taking this difference as an estimate of three-body dispersion for the closer trimers, and adding an Axilrod-Teller-Muto estimate of 0.13 kcal mol-1 for long-range contributions yields an overall value of 0.76 kcal mol-1 for three-body dispersion, a significantly smaller value than in several recent studies. [ABSTRACT FROM AUTHOR]

A systematic examination of the computational expense and accuracy of Symmetry-Adapted Perturbation Theory (SAPT) for the prediction of non-covalent interaction energies is provided with respect to both method [SAPT0, DFT-SAPT, SAPT2, SAPT2+, SAPT2+(3), and SAPT2+3; with and without CCD dispersion for the last three] and basis set [Dunning cc-pVDZ through aug-cc-pV5Z wherever computationally tractable, including truncations of diffuse basis functions]. To improve accuracy for hydrogen-bonded systems, we also include two corrections based on exchange-scaling (sSAPT0) and the supermolecular MP2 interaction energy (δMP2). When considering the best error performance relative to computational effort, we recommend as the gold, silver, and bronze standard of SAPT: SAPT2+(3)δMP2/aug-cc-pVTZ, SAPT2+/aug-cc-pVDZ, and sSAPT0/jun-ccpVDZ. Their respective mean absolute errors in interaction energy across the S22, HBC6, NBC10, and HSG databases are 0.15 (62.9), 0.30 (4.4), and 0.49 kcal mol-1 (0.03 h for adenine · thymine complex). [ABSTRACT FROM AUTHOR]

We investigate the torsion potentials in two prototypical π-conjugated polymers, polyacetylene and polydiacetylene, as a function of chain length using different flavors of density functional theory. Our study provides a quantitative analysis of the delocalization error in standard semilocal and hybrid density functionals and demonstrates how it can influence structural and thermodynamic properties. The delocalization error is quantified by evaluating the many-electron self-interaction error (MESIE) for fractional electron numbers, which allows us to establish a direct connection between the MESIE and the error in the torsion barriers. The use of non-empirically tuned long-range corrected hybrid functionals results in a very significant reduction of the MESIE and leads to an improved description of torsion barrier heights. In addition, we demonstrate how our analysis allows the determination of the effective conjugation length in polyacetylene and polydiacetylene chains. [ABSTRACT FROM AUTHOR]

Orbital-optimized coupled-electron pair theory [or simply 'optimized CEPA(0),' OCEPA(0), for short] and its analytic energy gradients are presented. For variational optimization of the molecular orbitals for the OCEPA(0) method, a Lagrangian-based approach is used along with an orbital direct inversion of the iterative subspace algorithm. The cost of the method is comparable to that of CCSD [O(N6) scaling] for energy computations. However, for analytic gradient computations the OCEPA(0) method is only half as expensive as CCSD since there is no need to solve the λ2-amplitude equation for OCEPA(0). The performance of the OCEPA(0) method is compared with that of the canonical MP2, CEPA(0), CCSD, and CCSD(T) methods, for equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions between radicals. For bond lengths of both closed and open-shell molecules, the OCEPA(0) method improves upon CEPA(0) and CCSD by 25%-43% and 38%-53%, respectively, with Dunning's cc-pCVQZ basis set. Especially for the open-shell test set, the performance of OCEPA(0) is comparable with that of CCSD(T) (ΔR is 0.0003 Å on average). For harmonic vibrational frequencies of closed-shell molecules, the OCEPA(0) method again outperforms CEPA(0) and CCSD by 33%-79% and 53%-79%, respectively. For harmonic vibrational frequencies of open-shell molecules, the mean absolute error (MAE) of the OCEPA(0) method (39 cm-1) is fortuitously even better than that of CCSD(T) (50 cm-1), while the MAEs of CEPA(0) (184 cm-1) and CCSD (84 cm-1) are considerably higher. For complete basis set estimates of hydrogen transfer reaction energies, the OCEPA(0) method again exhibits a substantially better performance than CEPA(0), providing a mean absolute error of 0.7 kcal mol-1, which is more than 6 times lower than that of CEPA(0) (4.6 kcal mol-1), and comparing to MP2 (7.7 kcal mol-1) there is a more than 10-fold reduction in errors. Whereas the MAE for the CCSD method is only 0.1 kcal mol-1 lower than that of OCEPA(0). Overall, the present application results indicate that the OCEPA(0) method is very promising not only for challenging open-shell systems but also for closed-shell molecules. [ABSTRACT FROM AUTHOR]

We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes. [ABSTRACT FROM AUTHOR]

Analytic energy gradients for the orbital-optimized second-order Mo\ller-Plesset perturbation theory (OMP2) are presented. The OMP2 method is applied to difficult chemical systems, including those where spatial or spin symmetry-breaking instabilities are observed. The performance of the OMP2 method is compared with that of second-order Mo\ller-Plesset perturbation theory (MP2) for investigating geometries and vibrational frequencies of the cis-HOOH+, trans-HOOH+, LiO2, C3+, and NO2 molecules. For harmonic vibrational frequencies, the OMP2 method eliminates the singularities arising from the abnormal response contributions observed for MP2 in case of symmetry-breaking problems, and provides significantly improved vibrational frequencies for the above molecules. We also consider the hydrogen transfer reactions between several free radicals, for which MP2 provides poor reaction energies. The OMP2 method again exhibits a considerably better performance than MP2, providing a mean absolute error of 2.3 kcal mol-1, which is more than 5 times lower than that of MP2 (13.2 kcal mol-1). Overall, the OMP2 method seems quite helpful for electronically challenging chemical systems such as symmetry-breaking molecules, hydrogen transfer reactions, or other cases where standard MP2 proves unreliable. For such systems, we recommend using OMP2 instead of MP2 as a more robust method with the same computational scaling. [ABSTRACT FROM AUTHOR]

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)]. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N5) effort if exact integrals are decomposed, or O(N4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry. [ABSTRACT FROM AUTHOR]

Predicting accurate bond-length alternations (BLAs) in long conjugated molecular chains has been a major challenge for electronic-structure theory for many decades. While Hartree-Fock (HF) overestimates BLA significantly, second-order perturbation theory and commonly used density functional theory (DFT) approaches typically underestimate it. Here, we discuss how this failure is related to the many-electron self-interaction error (MSIE), which is inherent to both HF and DFT approaches. We use tuned long-range corrected hybrids to minimize the MSIE for a series of polyenes. The key result is that the minimization of the MSIE alone does not yield accurate BLAs. On the other hand, if the range-separation parameter is tuned to yield accurate BLAs, we obtain a significant MSIE that grows with chain length. Our findings demonstrate that reducing the MSIE is one but not the only important aspect necessary to obtain accurate BLAs from density functional theory. [ABSTRACT FROM AUTHOR]

In benchmark-quality studies of non-covalent interactions, it is common to estimate interaction energies at the complete basis set (CBS) coupled-cluster through perturbative triples [CCSD(T)] level of theory by adding to CBS second-order perturbation theory (MP2) a 'coupled-cluster correction,' δMP2CCSD(T), evaluated in a modest basis set. This work illustrates that commonly used basis sets such as 6-31G*(0.25) can yield large, even wrongly signed, errors for δMP2CCSD(T) that vary significantly by binding motif. Double-ζ basis sets show more reliable results when used with explicitly correlated methods to form a δMP2-F12CCSD(T*)-F12 correction, yielding a mean absolute deviation of 0.11 kcal mol-1 for the S22 test set. Examining the coupled-cluster correction for basis sets up to sextuple-ζ in quality reveals that δMP2CCSD(T) converges monotonically only beyond a turning point at triple-ζ or quadruple-ζ quality. In consequence, CBS extrapolation of δMP2CCSD(T) corrections before the turning point, generally CBS (aug-cc-pVDZ,aug-cc-pVTZ), are found to be unreliable and often inferior to aug-cc-pVTZ alone, especially for hydrogen-bonding systems. Using the findings of this paper, we revise some recent benchmarks for non-covalent interactions, namely the S22, NBC10, HBC6, and HSG test sets. The maximum differences in the revised benchmarks are 0.080, 0.060, 0.257, and 0.102 kcal mol-1, respectively. [ABSTRACT FROM AUTHOR]

Symmetry-adapted perturbation theory (SAPT) provides a means of probing the fundamental nature of intermolecular interactions. Low-orders of SAPT (here, SAPT0) are especially attractive since they provide qualitative (sometimes quantitative) results while remaining tractable for large systems. The application of density fitting and Laplace transformation techniques to SAPT0 can significantly reduce the expense associated with these computations and make even larger systems accessible. We present new factorizations of the SAPT0 equations with density-fitted two-electron integrals and the first application of Laplace transformations of energy denominators to SAPT. The improved scalability of the DF-SAPT0 implementation allows it to be applied to systems with more than 200 atoms and 2800 basis functions. The Laplace-transformed energy denominators are compared to analogous partial Cholesky decompositions of the energy denominator tensor. Application of our new DF-SAPT0 program to the intercalation of DNA by proflavine has allowed us to determine the nature of the proflavine-DNA interaction. Overall, the proflavine-DNA interaction contains important contributions from both electrostatics and dispersion. The energetics of the intercalator interaction are are dominated by the stacking interactions (two-thirds of the total), but contain important contributions from the intercalator-backbone interactions. It is hypothesized that the geometry of the complex will be determined by the interactions of the intercalator with the backbone, because by shifting toward one side of the backbone, the intercalator can form two long hydrogen-bonding type interactions. The long-range interactions between the intercalator and the next-nearest base pairs appear to be negligible, justifying the use of truncated DNA models in computational studies of intercalation interaction energies. [ABSTRACT FROM AUTHOR]

Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order Mo\ller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply 'OD' and 'OMP2' for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H2O, three diatomics, and the O4+ molecule. Results demonstrate that the CCSD and OD methods give nearly identical results for H2O and diatomics; however, in symmetry-breaking problems as exemplified by O4+, the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle density matrices, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that are somewhat different than those of MP2 for most of the test cases considered (although they are similar for H2O). Bond lengths are somewhat longer, and vibrational frequencies somewhat smaller, for OMP2 compared to MP2. In the difficult case of O4+, results for several vibrational frequencies are significantly improved in going from MP2 to OMP2. [ABSTRACT FROM AUTHOR]

A systematic study of techniques for treating noncovalent interactions within the computationally efficient density functional theory (DFT) framework is presented through comparison to benchmark-quality evaluations of binding strength compiled for molecular complexes of diverse size and nature. In particular, the efficacy of functionals deliberately crafted to encompass long-range forces, a posteriori DFT+dispersion corrections (DFT-D2 and DFT-D3), and exchange-hole dipole moment (XDM) theory is assessed against a large collection (469 energy points) of reference interaction energies at the CCSD(T) level of theory extrapolated to the estimated complete basis set limit. The established S22 [revised in J. Chem. Phys. 132, 144104 (2010)] and JSCH test sets of minimum-energy structures, as well as collections of dispersion-bound (NBC10) and hydrogen-bonded (HBC6) dissociation curves and a pairwise decomposition of a protein-ligand reaction site (HSG), comprise the chemical systems for this work. From evaluations of accuracy, consistency, and efficiency for PBE-D, BP86-D, B97-D, PBE0-D, B3LYP-D, B970-D, M05-2X, M06-2X, ωB97X-D, B2PLYP-D, XYG3, and B3LYP-XDM methodologies, it is concluded that distinct, often contrasting, groups of these elicit the best performance within the accessible double-ζ or robust triple-ζ basis set regimes and among hydrogen-bonded or dispersion-dominated complexes. For overall results, M05-2X, B97-D3, and B970-D2 yield superior values in conjunction with aug-cc-pVDZ, for a mean absolute deviation of 0.41 - 0.49 kcal/mol, and B3LYP-D3, B97-D3, ωB97X-D, and B2PLYP-D3 dominate with aug-cc-pVTZ, affording, together with XYG3/6-311+G(3df,2p), a mean absolute deviation of 0.33 - 0.38 kcal/mol. [ABSTRACT FROM AUTHOR]

An accurate description of dispersion interactions is required for reliable theoretical studies of many noncovalent complexes. This can be obtained with the wave function-based formulation of symmetry-adapted perturbation theory (SAPT) provided that the contribution of triple excitations to dispersion is included. Unfortunately, this triples dispersion correction limits the applicability of SAPT due to its O(N7) scaling. The efficiency of the evaluation of this correction can be greatly improved by removing virtual orbitals from the computation. The error incurred from truncating the virtual space is reduced if second-order Mo\ller-Plesset perturbation theory (MP2) natural orbitals are used in place of the canonical Hartree-Fock molecular orbitals that are typically used. This approximation is further improved if the triples correction to dispersion is scaled to account for the smaller virtual space. If virtual MP2 natural orbitals are removed according to their occupation numbers, in practice, roughly half of the virtual orbitals can be removed (with the aug-cc-pVDZ basis set) with negligible errors if the remaining triples dispersion contribution is scaled. This typically leads to speedups of 15-20 times for the cases considered here. By combining the truncated virtual space with the frozen core approximation, the triples correction can be evaluated approximately 50 times faster than the canonical computation. These approximations cause less than 1% error (or at most 0.02 kcal mol-1) for the cases considered. Truncation of greater fractions of the virtual space is possible for larger basis sets (leading to speedups of over 40 times before additional speedups from the frozen core approximation). [ABSTRACT FROM AUTHOR]

Symmetry-adapted perturbation theory (SAPT) offers insight into the nature of intermolecular interactions. In addition, accurate energies can be obtained from the wave function-based variant of SAPT provided that intramonomer electron correlation effects are included. We apply density-fitting (DF) approximations to the intramonomer correlation corrections in SAPT. The introduction of this approximation leads to an improvement in the computational cost of SAPT by reducing the scaling of certain SAPT terms, reducing the amount of disk I/O, and avoiding the explicit computation of certain types of MO integrals. We have implemented all the intramonomer correlation corrections to SAPT through second-order under the DF approximation. Additionally, leading third-order terms are also implemented. The accuracy of this truncation of SAPT is tested against the S22 test set of Hobza and co-workers [Phys. Chem. Chem. Phys. 8, 1985 (2006)]. When the intramonomer corrections to dispersion are included in SAPT, a mean absolute deviation of 0.3–0.4 kcal mol-1 is observed for the S22 test set when using an aug-cc-pVDZ basis. The computations on the adenine-thymine complexes in the S22 test set with an aug-cc-pVDZ basis represent the largest SAPT computations to date that include this degree of intramonomer correlation. Computations of this size can now be performed routinely with our newly developed DF-SAPT program. [ABSTRACT FROM AUTHOR]

Density fitting (DF) approximations have been used to increase the efficiency of several quantum mechanical methods. In this work, we apply DF and a related approach, Cholesky decomposition (CD), to wave function-based symmetry-adapted perturbation theory (SAPT). We also test the one-center approximation to the Cholesky decomposition. The DF and CD approximations lead to a dramatic improvement in the overall computational cost of SAPT, while introducing negligible errors. For typical target accuracies, the Cholesky basis needed is noticeably smaller than the DF basis (although the cost of constructing the Cholesky vectors is slightly greater than that of constructing the three-index DF integrals). The SAPT program developed in this work is applied to the interactions between acenes previously studied by Grimme [Angew. Chem., Int. Ed. 47, 3430 (2008)], expanding the cases studied by adding the pentacene dimer. The SAPT decomposition of the acene interactions provides a more realistic picture of the interactions than that from the energy decomposition analysis previously reported. The data suggest that parallel-displaced and T-shaped acene dimers both feature a special stabilizing π-π interaction arising from electron correlation terms which are significantly more stabilizing than expected on the basis of pairwise -C6R-6 estimates. These terms are qualitatively the same in T-shaped as in parallel-displaced geometries, although they are roughly a factor of 2 smaller in T-shaped geometries because of the larger distances between the intermolecular pairs of electrons. [ABSTRACT FROM AUTHOR]