Structure of [18]Annulene Revisited: Challenges for Computing Benzenoid Systems.

For cyclic conjugated structures, erratic computational results have been obtained with Hartree-Fock (HF) molecular orbital (MO) methods as well as density functional theory (DFT) with large HF-exchange contributions. In this work, the reasons for this unreliability are explored. Extensive computations on [18]annulene and related compounds highlight the pitfalls to be avoided and the due diligence required for such computational investigations. In particular, a careful examination of the MO singlet-stability eigenvalues is recommended. The appearance of negative eigenvalues is not (necessarily) problematic, but near-zero (positive or negative) eigenvalues can lead to dramatic errors in vibrational frequencies and related properties. DFT approaches with a lower HF admixture generally appear more robust in this regard for the description of benzenoid structures, although they may exaggerate the tendency toward planarity and C-C bond-equalization. For the iconic [18]annulene, the results support a nonplanar equilibrium structure. The density-fitted frozen natural orbital coupled-cluster singles and doubles with perturbative triples [DF-FNO CCSD(T)] method of electron correlation with an aug-pVQZ/aug-pVTZ basis set places the C2 global minimum 1.1 kcal mol-1 below the D6h stationary point.

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.

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.

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.

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.

Competition Between π-π and C-H/π Interactions: A Comparison of the Structural and Electronic Properties of Alkoxy-Substituted 1,8-Bis((propyloxyphenyl)ethynyl)naphthalenes.

The structural and electronic consequences of π-π and C-H/π interactions in two alkoxy-substituted 1,8-bis- ((propyloxyphenyl)ethynyl)naphthalenes are explored by using X-ray crystallography and electronic structure computations. The crystal structure of analogue 4, bearing an alkoxy side chain in the 4-position of each of the phenyl rings, adopts a π-stacked geometry, whereas analogue 8, bearing alkoxy groups at both the 2- and the 5-positions of each ring, has a geometry in which the rings are splayed away from a π-stacked arrangement. Symmetry-adapted perturbation theory analysis was performed on the two analogues to evaluate the interactions between the phenylethynyl arms in each molecule in terms of electrostatic, steric, polarization, and London dispersion components. The computations support the expectation that the π-stacked geometry of the alkoxyphenyl units in 4 is simply a consequence of maximizing π-π interactions. However, the splayed geometry of 8 results from a more subtle competition between different noncovalent interactions: this geometry provides a favorable anti-alignment of C-O bond dipoles, and two C-H/π interactions in which hydrogen atoms of the alkyl side chains interact favorably with the π electrons of the other phenyl ring. These favorable interactions overcome competing π-π interactions to give rise to a geometry in which the phenylethynyl substituents are in an offset, unstacked arrangement.

A coupled cluster benchmark study of the electronic spectrum of the allyl radical.

We have investigated 15 excited states of the allyl radical, including the lowest three valence states (two doublets and one quartet) and the n = 3 Ry series, using coupled cluster methods that approximate the correlation effects of connected triple excitations. The quality of the excitation energies is measured on the basis of comparison to existing theoretical and experimental data, as well as on the basis of three diagnostics related to spin contamination and the overall level of excitation of a given state. Basis-set effects are significant for states exhibiting substantial Rydberg character, and the use of molecule-centered diffuse functions appears to provide an accurate description of such states, while avoiding the computational expense of basis sets in which diffuse functions are added to every atom in the molecule. In contrast to earlier observations for linear carbon-chain radicals, coupled cluster methods compare well to both theoretical predictions and experimental band origins, where discrepancies in the latter are sometimes attributable to structural relaxation in the excited state. One of the three lowest (2)B(1) excited states exhibits a twisting of the terminal methylene groups to yield a C(2)-symmetry minimum. The most challenging states for coupled cluster methods are of A(2) symmetry, where both spin contamination and basis-set effects are appreciable.

A benchmark study of the vertical electronic spectra of the linear chain radicals C(2)H and C(4)H.

The ability of coupled-cluster models to predict vertical excitation energies is tested on the electronic states of carbon-chain radicals of particular relevance to interstellar chemistry. Using spin-unrestricted and -restricted reference wave functions, the coupled-cluster singles and doubles (CCSD) model and a triples-including model (CC3) are tested on the sigma radicals C(2)H and C(4)H. Both molecules exhibit low-lying excited states with significant double-excitation character (as well as states of quartet multiplicity) and are thus challenging cases for excited-state approaches. In addition, we employ two diagnostics for the reliability of the CC results: the approximate excitation level (AEL) relative to the ground state and the difference between excitation energies obtained with spin-unrestricted and spin-restricted reference wave functions (the U-R difference). We find that CCSD yields poor excitation energies for states with AEL significantly larger than ca. 1.1 and/or large U-R differences, as well as for certain states exhibiting large spin contamination or other inadequacies in the reference determinant. In such cases, connected triple excitations can be included in the model and generally provide improved results. Furthermore, we find that large discrepancies exist between CC and multireference (MR) results for certain states. These disagreements are not related to basis-set effects, but likely arise from the lack of spin adaptation in conventional spin-orbital CC implementations and active space selection in the MR models.

On the accuracy of computed excited-state dipole moments.

The dipole moments of furan and pyrrole in many electronically excited singlet states have been determined using coupled cluster theory including large one-electron basis sets. The inclusion of connected triple excitations is shown to uniformly decrease the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) excitation energies by 0.04-0.24 eV, with an average reduction of 0.08 eV. Using a basis set larger than DZP (++)D (double-zeta plus polarization augmented with atom- and molecule-centered diffuse functions) uniformly increases the computed EOM-CCSD excitation energies by 0.03-0.29 eV, with an average increase of 0.20 eV. The corresponding shifts in excited-state dipole moments are more erratic. Including connected triple excitations changes the computed dipole moments by an rms amount of 0.17 au. More importantly, using a larger basis set shifts the dipole moments by an rms amount of 0.52 au, with an increase or a decrease being equally likely. The CC dipole moments are compared to those from time-dependent density functional theory (TD-DFT) computed by Burcl, Amos, and Handy [ Chem. Phys. Lett. 2002, 355, 8]. For 29 excited states of furan and pyrrole, the predicted TD-DFT dipole moments differ from the CC results by rms amounts of 1.6 au (HCTH functional) and 1.5 au (B97-1 functional). Including the asymptotic correction to TD-DFT developed by Tozer and Handy [ J. Chem. Phys. 1998, 109, 10180; J. Comput. Chem. 1999, 20, 106] reduces the rms differences for both functionals to 1.2 au. If those Rydberg excited states with very large polarizabilities are excluded, the rms differences from the CC results for the remaining 17 excited states become 1.31 au (HCTH) and 0.88 au (B97-1). For asymptotically corrected functionals and this subset of states, the rms differences from the CC results are only 0.54 au (HCTHc) and 0.34 au (B97-1c). Thus, the Tozer-Handy asymptotic correction for TD-DFT significantly improves the predictions of excited-state dipole moments. For excited states without very large polarizabilities, good agreement is achieved between excited-state dipole moments computed by coupled cluster theory and by the asymptotically corrected B97-1c density functional.

PSI3: an open-source Ab Initio electronic structure package.

PSI3 is a program system and development platform for ab initio molecular electronic structure computations. The package includes mature programming interfaces for parsing user input, accessing commonly used data such as basis-set information or molecular orbital coefficients, and retrieving and storing binary data (with no software limitations on file sizes or file-system-sizes), especially multi-index quantities such as electron repulsion integrals. This platform is useful for the rapid implementation of both standard quantum chemical methods, as well as the development of new models. Features that have already been implemented include Hartree-Fock, multiconfigurational self-consistent-field, second-order Møller-Plesset perturbation theory, coupled cluster, and configuration interaction wave functions. Distinctive capabilities include the ability to employ Gaussian basis functions with arbitrary angular momentum levels; linear R12 second-order perturbation theory; coupled cluster frequency-dependent response properties, including dipole polarizabilities and optical rotation; and diagonal Born-Oppenheimer corrections with correlated wave functions. This article describes the programming infrastructure and main features of the package. PSI3 is available free of charge through the open-source, GNU General Public License.

The lowest 2A' excited state of the water-hydroxyl complex.

Vertical and adiabatic excitation energies of the lowest (2)A(') excited state in the water-hydroxyl complex have been determined using coupled cluster, multireference configuration interaction, multireference perturbation theory, and density-functional methods. A significant redshift of about 0.4 eV in the vertical excitation energy of the complex compared to that of the hydroxyl radical monomer is found with the coupled cluster calculations validating previous results. Electronic excitation leads to a structure with near-equal sharing of the hydroxyl hydrogen by both oxygen atoms and a concomitantly large redshift of the adiabatic excitation energy of approximately 1 eV relative to the vertical excitation energy. The combination of redshifts ensures that the electronic transition in the complex lies well outside the equivalent excitation in the hydroxyl radical monomer. The complex is approximately five times more strongly bound in the excited state than in the ground state.

Application of equation-of-motion coupled-cluster methods to low-lying singlet and triplet electronic states of HBO and BOH.

The equilibrium structures and physical properties of the X (1)sigma(+) linear electronic states, linear excited singlet and triplet electronic states of hydroboron monoxide (HBO) (A (1)sigma(-), B (1)delta, a (3)sigma(+), and b (3)delta) and boron hydroxide (BOH) (A (1)sigma(+), B (1)Pi, and b (3)Pi), and their bent counterparts (HBO a (3)A('), b (3)A("), A (1)A("), B (1)A(') and BOH X (1)A('), b (3)A('), c (3)A("), A (1)A('), B (1)A('), C (1)A(")) are investigated using excited electronic state ab initio equation-of-motion coupled-cluster (EOM-CC) methods. A new implementation of open-shell EOM-CC including iterative partial triple excitations (EOM-CC3) was tested. Coupled-cluster wave functions with single and double excitations (CCSD), single, double, and iterative partial triple excitations (CC3), and single, double, and full triple excitations (CCSDT) are employed with the correlation-consistent quadruple and quintuple zeta basis sets. The linear HBO X (1)sigma(+) state is predicted to lie 48.3 kcal mol(-1) (2.09 eV) lower in energy than the BOH X (1)sigma(+) linear stationary point at the CCSDT level of theory. The CCSDT BOH barrier to linearity is predicted to lie 3.7 kcal mol(-1) (0.16 eV). With a harmonic zero-point vibrational energy correction, the HBO X (1)sigma(+)-BOH X (1)A(') energy difference is 45.2 kcal mol(-1) (1.96 eV). The lowest triplet excited electronic state of HBO, a (3)A('), has a predicted excitation energy (T(e)) of 115 kcal mol(-1) (4.97 eV) from the HBO ground state minimum, while the lowest-bound BOH excited electronic state, b (3)A('), has a T(e) of 70.2 kcal mol(-1) (3.04 eV) with respect to BOH X (1)A('). The T(e) values predicted for the lowest singlet excited states are A (1)A(")<--X (1)sigma(+)=139 kcal mol(-1) (6.01 eV) for HBO and A (1)A(')<--X (1)A(')=102 kcal mol(-1) (4.42 eV) for BOH. Also for BOH, the triplet vertical transition energies are b (3)A(')<--X (1)A(')=71.4 kcal mol(-1) (3.10 eV) and c (3)A(")<--X (1)A(')=87.2 kcal mol(-1) (3.78 eV).

Coupled cluster methods including triple excitations for excited states of radicals.

We report an extension of the coupled cluster iterative-triples model, CC3, to excited states of open-shell molecules, including radicals. We define the method for both spin-unrestricted Hartree-Fock (UHF) and spin-restricted open-shell Hartree-Fock (ROHF) reference determinants and discuss its efficient implementation in the PSI3 program package. The program is streamlined to use at most O(N(7)) computational steps and avoids storage of the triple-excitation amplitudes for both the ground- and excited-state calculations. The excitation-energy program makes use of a Lowdin projection formalism (comparable to that of earlier implementations) that allows computational reduction of the Davidson algorithm to only the single- and double-excitation space, but limits the calculation to only one excited state at a time. However, a root-following algorithm may be used to compute energies for multiple states of the same symmetry. Benchmark applications of the new methods to the lowest valence (2)B(1) state of the allyl radical, low-lying states of the CH and CO(+) diatomics, and the nitromethyl radical show substantial improvement over ROHF- and UHF-based CCSD excitation energies for states with strong double-excitation character or cases suffering from significant spin contamination. For the allyl radical, CC3 adiabatic excitation energies differ from experiment by less than 0.02 eV, while for the (2)Sigma(+) state of CH, significant errors of more than 0.4 eV remain.