Benchmark coupled-cluster lattice energy of crystalline benzene and assessment of multi-level approximations in the many-body expansion.

The many-body expansion (MBE) is promising for the efficient, parallel computation of lattice energies in organic crystals. Very high accuracy should be achievable by employing coupled-cluster singles, doubles, and perturbative triples at the complete basis set limit [CCSD(T)/CBS] for the dimers, trimers, and potentially tetramers resulting from the MBE, but such a brute-force approach seems impractical for crystals of all but the smallest molecules. Here, we investigate hybrid or multi-level approaches that employ CCSD(T)/CBS only for the closest dimers and trimers and utilize much faster methods like Møller-Plesset perturbation theory (MP2) for more distant dimers and trimers. For trimers, MP2 is supplemented with the Axilrod-Teller-Muto (ATM) model of three-body dispersion. MP2(+ATM) is shown to be a very effective replacement for CCSD(T)/CBS for all but the closest dimers and trimers. A limited investigation of tetramers using CCSD(T)/CBS suggests that the four-body contribution is entirely negligible. The large set of CCSD(T)/CBS dimer and trimer data should be valuable in benchmarking approximate methods for molecular crystals and allows us to see that a literature estimate of the core-valence contribution of the closest dimers to the lattice energy using just MP2 was overbinding by 0.5 kJ mol-1, and an estimate of the three-body contribution from the closest trimers using the T0 approximation in local CCSD(T) was underbinding by 0.7 kJ mol-1. Our CCSD(T)/CBS best estimate of the 0 K lattice energy is -54.01 kJ mol-1, compared to an estimated experimental value of -55.3 ± 2.2 kJ mol-1.

Optimized damping parameters for empirical dispersion corrections to symmetry-adapted perturbation theory.

Symmetry-adapted perturbation theory (SAPT) has become an invaluable tool for studying the fundamental nature of non-covalent interactions by directly computing the electrostatics, exchange (steric) repulsion, induction (polarization), and London dispersion contributions to the interaction energy using quantum mechanics. Further application of SAPT is primarily limited by its computational expense, where even its most affordable variant (SAPT0) scales as the fifth power of system size [O(N5)] due to the dispersion terms. The algorithmic scaling of SAPT0 is reduced from O(N5)→O(N4) by replacing these terms with the empirical D3 dispersion correction of Grimme and co-workers, forming a method that may be termed SAPT0-D3. Here, we optimize the damping parameters for the -D3 terms in SAPT0-D3 using a much larger training set than has previously been considered, namely, 8299 interaction energies computed at the complete-basis-set limit of coupled cluster through perturbative triples [CCSD(T)/CBS]. Perhaps surprisingly, with only three fitted parameters, SAPT0-D3 improves on the accuracy of SAPT0, reducing mean absolute errors from 0.61 to 0.49 kcal mol-1 over the full set of complexes. Additionally, SAPT0-D3 exhibits a nearly 2.5× speedup over conventional SAPT0 for systems with ∼300 atoms and is applied here to systems with up to 459 atoms. Finally, we have also implemented a functional group partitioning of the approach (F-SAPT0-D3) and applied it to determine important contacts in the binding of salbutamol to G-protein coupled ß1-adrenergic receptor in both active and inactive forms. SAPT0-D3 capabilities have been added to the open-source Psi4 software.

Quantum Chemistry Common Driver and Databases (QCDB) and Quantum Chemistry Engine (QCEngine): Automation and interoperability among computational chemistry programs.

Community efforts in the computational molecular sciences (CMS) are evolving toward modular, open, and interoperable interfaces that work with existing community codes to provide more functionality and composability than could be achieved with a single program. The Quantum Chemistry Common Driver and Databases (QCDB) project provides such capability through an application programming interface (API) that facilitates interoperability across multiple quantum chemistry software packages. In tandem with the Molecular Sciences Software Institute and their Quantum Chemistry Archive ecosystem, the unique functionalities of several CMS programs are integrated, including CFOUR, GAMESS, NWChem, OpenMM, Psi4, Qcore, TeraChem, and Turbomole, to provide common computational functions, i.e., energy, gradient, and Hessian computations as well as molecular properties such as atomic charges and vibrational frequency analysis. Both standard users and power users benefit from adopting these APIs as they lower the language barrier of input styles and enable a standard layout of variables and data. These designs allow end-to-end interoperable programming of complex computations and provide best practices options by default.

Efficient and automated computation of accurate molecular geometries using focal-point approximations to large-basis coupled-cluster theory.

The focal-point approach, combining several quantum chemistry computations to estimate a more accurate computation at a lower expense, is effective and commonly used for energies. However, it has not yet been widely adopted for properties such as geometries. Here, we examine several focal-point methods combining Møller-Plesset perturbation theory (MP2 and MP2.5) with coupled-cluster theory through perturbative triples [CCSD(T)] for their effectiveness in geometry optimizations using a new driver for the Psi4 electronic structure program that efficiently automates the computation of composite-energy gradients. The test set consists of 94 closed-shell molecules containing first- and/or second-row elements. The focal-point methods utilized combinations of correlation-consistent basis sets cc-pV(X+d)Z and heavy-aug-cc-pV(X+d)Z (X = D, T, Q, 5, 6). Focal-point geometries were compared to those from conventional CCSD(T) using basis sets up to heavy-aug-cc-pV5Z and to geometries from explicitly correlated CCSD(T)-F12 using the cc-pVXZ-F12 (X = D, T) basis sets. All results were compared to reference geometries reported by Karton et al. [J. Chem. Phys. 145, 104101 (2016)] at the CCSD(T)/heavy-aug-cc-pV6Z level of theory. In general, focal-point methods based on an estimate of the MP2 complete-basis-set limit, with a coupled-cluster correction evaluated in a (heavy-aug-)cc-pVXZ basis, are of superior quality to conventional CCSD(T)/(heavy-aug-)cc-pV(X+1)Z and sometimes approach the errors of CCSD(T)/(heavy-aug-)cc-pV(X+2)Z. However, the focal-point methods are much faster computationally. For the benzene molecule, the gradient of such a focal-point approach requires only 4.5% of the computation time of a conventional CCSD(T)/cc-pVTZ gradient and only 0.4% of the time of a CCSD(T)/cc-pVQZ gradient.

Psi4 1.4: Open-source software for high-throughput quantum chemistry.

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

CrystaLattE: Automated computation of lattice energies of organic crystals exploiting the many-body expansion to achieve dual-level parallelism.

We present an algorithm to compute the lattice energies of molecular crystals based on the many-body cluster expansion. The required computations on dimers, trimers, etc., within the crystal are independent of each other, leading to a naturally parallel approach. The algorithm exploits the long-range three-dimensional periodic order of crystals to automatically detect and avoid redundant or unnecessary computations. For this purpose, Coulomb-matrix descriptors from machine learning applications are found to be efficient in determining whether two N-mers are identical. The algorithm is implemented as an open-source Python program, CrystaLattE, that uses some of the features of the Quantum Chemistry Common Driver and Databases library. CrystaLattE is initially interfaced with the quantum chemistry package Psi4. With CrystaLattE, we have applied the fast, dispersion-corrected Hartree-Fock method HF-3c to the lattice energy of crystalline benzene. Including all 73 symmetry-unique dimers and 7130 symmetry-unique trimers that can be formed from molecules within a 15 Å cutoff from a central reference monomer, HF-3c plus an Axilrod-Teller-Muto estimate of three-body dispersion exhibits an error of only -1.0 kJ mol-1 vs the estimated 0 K experimental lattice energy of -55.3 ± 2.2 kJ mol-1. The convergence of the HF-3c two- and three-body contributions to the lattice energy as a function of intermonomer distance is examined.

The BioFragment Database (BFDb): An open-data platform for computational chemistry analysis of noncovalent interactions.

Accurate potential energy models are necessary for reliable atomistic simulations of chemical phenomena. In the realm of biomolecular modeling, large systems like proteins comprise very many noncovalent interactions (NCIs) that can contribute to the protein's stability and structure. This work presents two high-quality chemical databases of common fragment interactions in biomolecular systems as extracted from high-resolution Protein DataBank crystal structures: 3380 sidechain-sidechain interactions and 100 backbone-backbone interactions that inaugurate the BioFragment Database (BFDb). Absolute interaction energies are generated with a computationally tractable explicitly correlated coupled cluster with perturbative triples [CCSD(T)-F12] "silver standard" (0.05 kcal/mol average error) for NCI that demands only a fraction of the cost of the conventional "gold standard," CCSD(T) at the complete basis set limit. By sampling extensively from biological environments, BFDb spans the natural diversity of protein NCI motifs and orientations. In addition to supplying a thorough assessment for lower scaling force-field (2), semi-empirical (3), density functional (244), and wavefunction (45) methods (comprising >1M interaction energies), BFDb provides interactive tools for running and manipulating the resulting large datasets and offers a valuable resource for potential energy model development and validation.

Counterion and substrate effects on barrier heights of the hydrolytic kinetic resolution of terminal epoxides catalyzed by Co(III)-salen.

Density functional theory (DFT) has been applied to the proposed rate-limiting step of the hydrolytic kinetic resolution (HKR) of terminal epoxides as catalyzed by Co-salen-X (X = counterion) in order to resolve questions surrounding the mechanism. The present results indicate that the bimetallic mechanism proposed by Jacobsen shows nonadditive, cooperative catalysis with a larger reduction in barrier height than the sum of the barrier height reductions from the two monometallic reaction pathways. We computed barrier heights for the reaction using several counterions (chloride, acetate, tosylate, and hydroxide). For the three counterions that are experimentally active (chloride, acetate, and tosylate) the barrier heights are 35, 38, and 34 kJ mol(-1), respectively, while for hydroxide it is 48 kJ mol(-1). The similarity of the barrier heights for chloride, acetate, and tosylate is in agreement with their similar peak reaction rates. The finding that Co-salen-X with these counterions leads to rather different overall reaction profiles suggests that they have quite different rates of reaction with epoxide to form the activated Co-salen-OH required for the bimetallic mechanism. Co-salen-OH is inactive as the sole catalyst for HKR, and this inactivity is ascribed to its larger barrier height for the ring-opening step, rather than to any inability to activate epoxide. Barrier heights were also computed using propylene oxide, 1-hexene oxide, and epichlorohydrin; propylene oxide and 1-hexene oxide have similar barrier heights, 35.5 and 33.2 kJ mol(-1), respectively, and epichlorohydrin has a significantly lower barrier height of 18.8 kJ mol(-1), which is qualitatively consistent with experiments showing faster reactions for epicholorohydrin than propylene oxide when catalyzed by Co-salen-OAc.

Appointing silver and bronze standards for noncovalent interactions: a comparison of spin-component-scaled (SCS), explicitly correlated (F12), and specialized wavefunction approaches.

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 ζ-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.

Levels of symmetry adapted perturbation theory (SAPT). I. Efficiency and performance for interaction energies.

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-cc-pVDZ. 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).

Buckyplates and buckybowls: examining the effects of curvature on π-π interactions.

π-π interactions are integral to many areas of chemistry, biochemistry, and materials science. Here we use electronic structure theory to analyze how π-π interactions change as the π-systems are curved in model complexes based on coronene and corannulene dimers. Curvature redistributes electronic charge in the π-cloud and creates a dipole moment in these systems, leading to enhanced intermolecular electrostatic interactions in the concave-convex (nested) geometries that are the focus of this work. Curvature of both monomers also has a geometric effect on the interaction by decreasing the average C-C distance between monomers and by increasing the magnitude of both favorable London dispersion interactions and unfavorable exchange-repulsion interactions. Overall, increasing curvature in nested π-π interactions leads to more favorable interaction energies regardless of the native state of the monomers, except at short distances where the most highly curved systems are less favorable as exchange repulsion terms begin to dominate the interaction.

Basis set convergence of the coupled-cluster correction, δ(MP2)(CCSD(T)): best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases.

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," δ(MP2)(CCSD(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 δ(MP2)(CCSD(T)) that vary significantly by binding motif. Double-ζ basis sets show more reliable results when used with explicitly correlated methods to form a δ(MP2-F12)(CCSD(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 δ(MP2)(CCSD(T)) converges monotonically only beyond a turning point at triple-ζ or quadruple-ζ quality. In consequence, CBS extrapolation of δ(MP2)(CCSD(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.

Density-functional approaches to noncovalent interactions: a comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals.

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.

Vibrational specificity of proton-transfer dynamics in ground-state tropolone.

The vibrational dependence of large-amplitude proton transfer taking place in the ground electronic state (X1A1) of tropolone has been explored by implementing a coherent variant of the stimulated emission pumping (SEP) technique within the framework of two-color resonant four-wave mixing (TC-RFWM) spectroscopy. The lowest 1700 cm(-1) portion of this potential surface has been interrogated under ambient bulk-gas conditions, enabling rotationless term energies (Tv+) and tunneling-induced bifurcations Delta(v)X to be extracted for 43 assigned vibrational features of a1 and b2 symmetry. The resulting values of Delta(v)X reflect the state-specificity long attributed to the hydron-migration pathways of tropolone and range in magnitude from 0.0 cm(-1) to 17.8 cm(-1), where the former implies essentially complete quenching of unimolecular dynamics whilst the latter represents nearly a twenty-fold increase in reaction rate over that of the zero-point level. This vibrational mediation of tunneling behavior is discussed in terms of attendant atomic displacements and permutation-inversion symmetries, with choreographed motion of the five-member reaction site (C-O-H...O=C) found to exert the most significant influence on the efficacy of proton transfer.

Electronic structure and proton transfer in ground-state hexafluoroacetylacetone.

The ground electronic state (X(1)A(1)) of hexafluoroacetylacetone (HFAA) has been subjected to synergistic experimental and theoretical investigations designed to resolve controversies surrounding the nature of intramolecular hydrogen bonding for the enol tautomer. Cryogenic (93K) X-ray diffraction studies were conducted on single HFAA crystals grown in situ by means of the zone-melting technique, with the resulting electron density maps affording clear evidence for distinguishable O(1)-H and H...O(2) bonds that span an interoxygen distance of 2.680 +/- 0.003 A. Such laboratory findings have been corroborated by a variety of quantum chemical methods including Hartree-Fock (HF), density functional [DFT (B3LYP)], Møller-Plesset perturbation (MPn), and coupled cluster [CCSD, CCSD(T)] treatments built upon extensive sets of correlation-consistent basis functions. Geometry optimizations performed at the CCSD(T)/aug-cc-pVDZ level of theory predict an asymmetric (C(s)) equilibrium configuration characterized by an O...O donor-acceptor separation of 2.628 A. Similar analyses of the transition state for proton transfer reveal a symmetric (C(2v)) structure that presents a potential barrier of 21.29 kJ/mol (1779.7 cm(-1)) height. The emerging computational description of HFAA is in reasonable accord with crystallographic measurements and suggests a weakening of hydrogen-bond strength relative to that of the analogous acetylacetone molecule.

Dissection of rovibronic structure by polarization-resolved two-color resonant four-wave mixing spectroscopy.

A synergistic theoretical and experimental investigation of stimulated emission pumping (SEP) as implemented in the coherent framework of two-color resonant four-wave mixing (TC-RFWM) spectroscopy is presented, with special emphasis directed toward the identification of polarization geometries that can distinguish spectral features according to their attendant changes in rotational quantum numbers. A vector-recoupling formalism built upon a perturbative treatment of matter-field interactions and a state-multipole expansion of the density operator allowed the weak-field signal intensity to be cast in terms of a TC-RFWM response tensor, RQ(K)(epsilon4*epsilon3epsilon2*epsilon1;Jg,Je,Jh,Jf), which separates the transverse characteristics of the incident and generated electromagnetic waves (epsilon4*epsilon3epsilon2*epsilon1) from the angular momentum properties of the PUMP and DUMP resonances (Jg,Je,Jh,Jf). For an isolated SEP process induced in an isotropic medium, the criteria needed to discriminate against subsets of rovibronic structure were encoded in the roots of a single tensor element, R0(0)(epsilon4*epsilon3epsilon2*epsilon1;Jg,Je,Jh,Je). By assuming all optical fields to be polarized linearly and invoking the limit of high quantum numbers, specific angles of polarization for the detected signal field were found to suppress DUMP resonances selectively according to the nature of their rotational branch and the rotational branch of the meshing PUMP line. These predictions were corroborated by performing SEP measurements on the ground electronic potential energy surface of tropolone in two distinct regimes of vibrational excitation, with the near-ultraviolet 1B2-1A1 (pi*<--pi) absorption system affording the requisite PUMP and DUMP transitions.

An exploration of electronic structure and nuclear dynamics in tropolone: II. The A (1)B2 (pi* pi) excited state.

The first excited singlet state of tropolone (A (1)B(2)) and the attendant pi(*)<--pi electronic transition have been examined computationally by applying several quantum chemical treatments built upon the aug-cc-pVDZ basis set, including time-dependent density functional theory (TDDFT/B3LYP), configuration interaction singles with perturbative corrections [CIS and CIS(D)], and equation-of-motion coupled-cluster schemes [EOM-CCSD and CR-EOMCCSD(T)]. As in the case of the X (1)A(1) ground state [L. A. Burns, D. Murdock, and P. H. Vaccaro, J. Chem. Phys. 124, 204307 (2006)], geometry optimization procedures and harmonic force-field calculations predict the electronically excited potential surface to support a global minimum-energy configuration of rigorously planar (C(s)) symmetry. Minimal Hartree-Fock (HF/CIS) and density-functional (DFT/TDDFT) approaches yield inconsistent results for the X (1)A(1) and A (1)B(2) manifolds; however, coupled-cluster (CCSD/EOM-CCSD) methods give fully relaxed proton-transfer barrier heights of DeltaE(pt) (X)=3296.1 cm(-1) and DeltaE(pt) (A)=1270.6 cm(-1) that are in accordance with the experimentally observed increase in vibrationless tunneling splitting upon electronic excitation. Detailed analyses show that this reduction in DeltaE(pt) stems from a variety of complementary factors, most notably an overall contraction of the proton-transfer reaction site (whereby the equilibrium O...O donor-acceptor distance decreases from 2.53 to 2.46 A) and a concomitant shortening of the intramolecular hydrogen bond. Further refinement of A (1)B(2) energies through single-point perturbative triples corrections [CR-EOMCCSD(T)] leads to 1316.1 cm(-1) as the best current estimate for DeltaE(pt) (A). Direct comparison of the lowest-lying out-of-plane torsional mode [nu(39)(a(2))] for X (1)A(1) and A (1)B(2) tropolone reveals that its disparate nature (cf. nu(39) (X)=101.2 cm(-1) and nu(39) (A)=42.0 cm(-1)) mediates vibrational-averaging effects which can account for inertial defects extracted by rotationally resolved spectroscopic measurements.

Psi4NumPy: An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development.

Psi4NumPy demonstrates the use of efficient computational kernels from the open-source Psi4 program through the popular NumPy library for linear algebra in Python to facilitate the rapid development of clear, understandable Python computer code for new quantum chemical methods, while maintaining a relatively low execution time. Using these tools, reference implementations have been created for a number of methods, including self-consistent field (SCF), SCF response, many-body perturbation theory, coupled-cluster theory, configuration interaction, and symmetry-adapted perturbation theory. Furthermore, several reference codes have been integrated into Jupyter notebooks, allowing background, underlying theory, and formula information to be associated with the implementation. Psi4NumPy tools and associated reference implementations can lower the barrier for future development of quantum chemistry methods. These implementations also demonstrate the power of the hybrid C++/Python programming approach employed by the Psi4 program.

Comparison of Explicitly Correlated Methods for Computing High-Accuracy Benchmark Energies for Noncovalent Interactions.

The reliability of explicitly correlated methods for providing benchmark-quality noncovalent interaction energies was tested at various levels of theory and compared to estimates of the complete basis set (CBS) limit. For all systems of the A24 test set, computations were performed using both aug-cc-pVXZ (aXZ; X = D, T, Q, 5) basis sets and specialized cc-pVXZ-F12 (XZ-F12; X = D, T, Q, 5) basis sets paired with explicitly correlated coupled cluster singles and doubles [CCSD-F12n (n = a, b, c)] with triple excitations treated by the canonical perturbative method and scaled to compensate for their lack of explicit correlation [(T**)]. Results show that aXZ basis sets produce smaller errors versus the CBS limit than XZ-F12 basis sets. The F12b ansatz results in the lowest average errors for aTZ and larger basis sets, while F12a is best for double-ζ basis sets. When using aXZ basis sets (X ≥ 3), convergence is achieved from above for F12b and F12c ansatzë and from below for F12a. The CCSD(T**)-F12b/aXZ approach converges quicker with respect to basis than any other combination, although the performance of CCSD(T**)-F12c/aXZ is very similar. Both CCSD(T**)-F12b/aTZ and focal point schemes employing density-fitted, frozen natural orbital [DF-FNO] CCSD(T)/aTZ exhibit similar accuracy and computational cost, and both are much more computationally efficient than large-basis conventional CCSD(T) computations of similar accuracy.

Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability.

Psi4 is an ab initio electronic structure program providing methods such as Hartree-Fock, density functional theory, configuration interaction, and coupled-cluster theory. The 1.1 release represents a major update meant to automate complex tasks, such as geometry optimization using complete-basis-set extrapolation or focal-point methods. Conversion of the top-level code to a Python module means that Psi4 can now be used in complex workflows alongside other Python tools. Several new features have been added with the aid of libraries providing easy access to techniques such as density fitting, Cholesky decomposition, and Laplace denominators. The build system has been completely rewritten to simplify interoperability with independent, reusable software components for quantum chemistry. Finally, a wide range of new theoretical methods and analyses have been added to the code base, including functional-group and open-shell symmetry adapted perturbation theory, density-fitted coupled cluster with frozen natural orbitals, orbital-optimized perturbation and coupled-cluster methods (e.g., OO-MP2 and OO-LCCD), density-fitted multiconfigurational self-consistent field, density cumulant functional theory, algebraic-diagrammatic construction excited states, improvements to the geometry optimizer, and the "X2C" approach to relativistic corrections, among many other improvements.