Diffuse Basis Sets Research Articles

Free Cyclooctatetraene Dianion: Planarity, Aromaticity, and Theoretical Challenges.

The planarity and 10 π-electron aromaticity of the free cyclooctatetraene dianion (C8H82–, COT2–) have been questioned recently on the basis of conflicting density functional and second-order Moller–Plesset perturbation computations. Rigorous coupled-cluster methods are employed here to establish the structure and properties of COT2–. Like many multiply charged anions, COT2– exists in isolation only as a short-lived resonance state lying above neutral COT. Wave function stability analysis demonstrates that predictions of nonplanar COT2– rings are artifacts of using overly diffuse basis sets. The resulting broken-symmetry wave functions are not characteristic of COT2– but mainly describe COT in a continuum of free electrons. All-electron coupled cluster theory extended through triple excitations [AE-CCSD(T)] yields a planar D8h symmetry COT2– structure. Final focal point analyses place the COT2– resonance state 61.6 kcal mol–1 above neutral COT. Nonetheless, COT2– exhibits structural, magnetic, and energet...

Assessment of Kohn–Sham density functional theory and Møller–Plesset perturbation theory for ionic liquids

We present high-level benchmark calculations of interaction energies of 236 ion pair structures of ionic liquids constituting a new IL-2013 set. 33 different approaches using various basis sets are validated against these benchmark data. Overall, traditional functionals like B3LYP, without an explicit dispersion correction, should be avoided when investigating ionic liquids. We can recommend the third version of Grimme's empirical dispersion correction (DFT-D3) and the LC-BOP functional, as well as most functionals of the Minnesota family of the M0X type. Our results highlight the importance of diffuse basis set functions for the accurate prediction of the IL energetics using any DFT functional. The best combination of reasonable accuracy and reasonable cost was found to be the M06-L functional in combination with the 6-31++G** basis set, producing a remarkable mean absolute deviation of only 4.2 kJ mol(-1) and a maximum deviation of -12.5 kJ mol(-1). Second-order Møller-Plesset perturbation theory (MP2) in combination with counterpoise-corrected triple-ζ basis sets can also be recommended for reliable calculations of energetics of ionic liquids.

CAP/SAC-CI method for calculating resonance states of metastable anions

The complex absorbing potential (CAP)/symmetry-adapted cluster-configuration interaction (SAC-CI) method has been developed to investigate resonance states of metastable anions. The method has been implemented in the projected scheme and applied to the π∗ resonance state of formaldehyde. The dependence on both valence and diffuse basis sets up to g-function, the number of SAC-CI states in the projection, and the effect of perturbation selection are examined. The potential energy curve and decay width are calculated in the C–O stretching coordinate, and the Franck–Condon factors for transitions from neutral to resonance state are evaluated to interpret the electron transmission (ET) spectrum.

On the potential application of DFT methods in predicting the interaction-induced electric properties of molecular complexes. Molecular H-bonded chains as a case of study

A detailed analysis of the selected DFT functionals for the calculations of interaction-induced dipole moment, polarizability and first-order hyperpolarizability has been carried out. The hydrogen-bonded model chains consisting of HF, H2CO and H3N molecules have been chosen as a case study. The calculations of the components of the static electric properties using the diffuse Dunning’s basis set (aug-cc-pVDZ) have been performed employing different types of density functionals (B3LYP, LC-BLYP, PBE0, M06-2X and CAM-B3LYP). Obtained results have been compared with those gained at the CCSD(T) level of theory. The counterpoise correction scheme, namely site-site function counterpoise, has been applied in order to eliminate basis set superposition error. The performed tests allow to conclude that the DFT functionals can provide a useful tool for prediction of the interaction-induced electric properties, however a caution has to be urged to their decomposition to the two- and many-body terms. Figure Hydrogen-bonded model chains consisting of HF, H2CO and H3N molecules

Can a Dipole-Bound Electron Form a Pseudo-Atom? An Atoms-In-Molecules Study of the Hydrated Electron

Non-nuclear local maxima, or attractors, of electron density are a rare but very interesting feature of the electron density distribution in molecules and solids. Recently, non-nuclear attractors (NNAs) and the corresponding pseudoatoms of electron density have been identified with the quantum theory of atoms in molecules for some anionic clusters formed by several polar solvent molecules and an excess electron bound in either a solvated-electron or dipole-bound fashion. This contribution reports a detailed study of the topology of the electron density for a series of dipole-bound water cluster anions, as calculated with Hartree-Fock, Møller-Plesset perturbation theory, and coupled-cluster methods together with basis sets augmented with extra diffuse basis functions to accommodate the excess electron. For dipole-bound clusters, electron densities obtained with insufficient inclusion of electron correlation effects and tight basis sets feature a well-pronounced pseudoatom due to the excess electron, which ultimately disappears when a higher level of electronic structure theory and a more diffuse basis set are used. On the other hand, for solvated-electron clusters, where the excess electron is surrounded by solvent molecules, the existence of NNAs does not seem to be an artifact of the method employed, but rather a genuine feature of the electron density distribution. Pseudoatoms of electron density thus appear to be an exclusive feature of confined environments and are unlikely to be found on the tip of a cluster dipole or on solid surfaces.

The Ethidium–UA/AU Intercalation Site: Effect of Model Fragmentation and Backbone Charge State

We report a systematic analysis of the intermolecular interactions of cationic ethidium intercalated into a UA/AU step of RNA for a single conformation based on crystallographic coordinates. Interaction energies at the MP2/6-31G** level were partitioned into electrostatic, exchange, delocalization, and correlation components. Various pairwise interaction models built from chemically intuitive fragments reproduce within a few percent values obtained when treating the intercalation site as a whole. Gas phase results are very sensitive to the charge state of the two phosphate groups, with the electrostatic term nearly tripling when the counterions are removed. But this is largely compensated by solvation, an effect represented here within the polarizable continuum model. In a few cases, more diffuse and larger basis sets as well as QCISD(T) corrections were applied in an effort to estimate plausible ethidium-nucleobase electron correlation effects.

Theoretical study of new acceptor and donor molecules based on polycyclic aromatic hydrocarbons

Functionalized polycyclic aromatic hydrocarbons (PAHs) are an interesting class of molecules in which the electronic state of the graphene-like hydrocarbon part is tuned by the functional group. Searching for new types of donor and acceptor molecules, a set of new PAHs has recently been investigated experimentally using ultraviolet photoelectron spectroscopy (UPS). In this work, the electronic structure of the PAHs is studied theoretically with the help of B3LYP hybrid density functionals. Using the ΔSCF method, electron binding energies have been determined which affirm, specify and complement the UPS data. Symmetry properties of molecular orbitals are analyzed for a categorization and an estimate of the related signal strength. While σ-like orbitals are difficult to detect in UPS spectra of condensed film, calculation provides a detailed insight into the hidden parts of the electronic structure of donor and acceptor molecules. In addition, a diffuse basis set (6-311++G**) was used to calculate electron affinity and LUMO eigenvalues. The calculated electron affinity (EA) provides a classification of the donor/acceptor properties of the studied molecules. Coronene-hexaone shows a high EA, comparable to TCNQ, which is a well-known classical acceptor. Calculated HOMO–LUMO gaps using the related eigenvalues have a good agreement with the experimental lowest excitation energies. TD-DFT also accurately predicts the measured optical gap.

Property-optimized Gaussian basis sets for molecular response calculations

With recent advances in electronic structure methods, first-principles calculations of electronic response properties, such as linear and nonlinear polarizabilities, have become possible for molecules with more than 100 atoms. Basis set incompleteness is typically the main source of error in such calculations since traditional diffuse augmented basis sets are too costly to use or suffer from near linear dependence. To address this problem, we construct the first comprehensive set of property-optimized augmented basis sets for elements H-Rn except lanthanides. The new basis sets build on the Karlsruhe segmented contracted basis sets of split-valence to quadruple-zeta valence quality and add a small number of moderately diffuse basis functions. The exponents are determined variationally by maximization of atomic Hartree-Fock polarizabilities using analytical derivative methods. The performance of the resulting basis sets is assessed using a set of 313 molecular static Hartree-Fock polarizabilities. The mean absolute basis set errors are 3.6%, 1.1%, and 0.3% for property-optimized basis sets of split-valence, triple-zeta, and quadruple-zeta valence quality, respectively. Density functional and second-order Møller-Plesset polarizabilities show similar basis set convergence. We demonstrate the efficiency of our basis sets by computing static polarizabilities of icosahedral fullerenes up to C(720) using hybrid density functional theory.

Negative Electron Affinities from DFT: Fluorination of Ethylene

Four simple density functional theory methods are investigated to assess how well they can describe subtle variations in negative vertical electron affinities arising due to the successive fluorination of ethylene, where the magnitude of the variations is well below the absolute accuracy of the methods. Three of the approaches (two based on Koopmans' theorem and one using a potential wall) are able to describe the trends in the affinities using both compact and very diffuse basis sets. The best results are obtained using the potential wall. The fourth approach uses a conventional energy difference evaluation, which is only applicable when the basis set is compact; the breakdown upon addition of diffuse functions is strikingly illustrated. The results are interpreted in terms of the apatial extent of the relevant orbitals and the signs and values of the orbital energies. The study highlights the potential predictive value of simple DFT methods for describing trends in negative affinities.

Basis set effects on the hyperpolarizability of CHCl3: Gaussian-type orbitals, numerical basis sets and real-space grids

Calculations of the hyperpolarizability are typically much more difficult to converge with basis set size than the linear polarizability. In order to understand these convergence issues and hence obtain accurate ab initio values, we compare calculations of the static hyperpolarizability of the gas-phase chloroform molecule (CHCl(3)) using three different kinds of basis sets: Gaussian-type orbitals, numerical basis sets, and real-space grids. Although all of these methods can yield similar results, surprisingly large, diffuse basis sets are needed to achieve convergence to comparable values. These results are interpreted in terms of local polarizability and hyperpolarizability densities. We find that the hyperpolarizability is very sensitive to the molecular structure, and we also assess the significance of vibrational contributions and frequency dispersion.

Studies on structures, energetics, and electron affinities of As–nucleobases and their anions with density functional theory

The structures of the As–nucleobases (As–adenine, –guanine, –cytosine, –thymine, and –uracil) and their anions are studied at the density functional B3LYP with a double-ζ plus diffuse (DZP++) basis set. The lowest energy structures of these complexes are presented. For the case of neutral systems, a strong association between arsenic atom and nucleobases is found and the ground state structures are R–As–H (R = nucleobases radical) complexes. For anions, the most stable structures are also R–As–H forms, but their association sites are different from corresponding neutrals with the exception of As–adenine. The extra electron of the anions is mainly localized on the arsenic atom. The adiabatic electron affinity (AEA), the vertical electron affinity (VEA), and the vertical detachment energy (VDE) for these complexes are reported. The formation energies of these complexes are also estimated, respectively, in order to examine relative stabilities. The stability order is As–guanine > As–adenine > As–uracil > As–cytosine > As–thymine.

Reactivity of the NO Dimer: On the Role of the Triplet Electronic States

We performed ab initio calculations to investigate the lowest triplet and singlet electronic states of the NO dimer and their mutual spin-orbit couplings. The electronic structure calculations are done using multiconfigurational approaches and a large diffuse basis set. A high density of electronic states is found favoring their mutual interactions by vibronic and spin-orbit couplings. We used our potential curves and spin-orbit couplings to discuss the mechanisms for the IR dissociation and the UV photodissociation of the NO dimer and the electronic de-excitation of NO (A(2)Sigma(+)) after collision with NO (X(2)Pi). For these reactions, multistep pathways, which involve the long-range and the molecular regions of the potential energy surfaces of the triplet and singlet electronic states of N(2)O(2), are suggested. A qualitative agreement between our findings and previous experimental assumptions is found.

A B3LYP and MP2 theoretical investigation into host-guest interaction between calix[4]arene and Li+ or Na+

The DFT-B3LYP and MP2 methods with 6-311G** and 6-311++G** basis sets have been applied to study the complexation energies of the host-guest complexes between the cone calix[4]arene and Li(+) or Na(+) on the B3LYP optimized geometries. A comparison of the complexation energies obtained from the MP2(full) with those from MP2(fc) method is also carried out. The result shows that it is essential to introduce the diffuse basis set into the geometry optimizations and complexation energy calculations of the alkali-metal cation-pi interaction complexes of calix[4]arene, and the D (e) values show a maximum of 21.13 kJ mol(-1) (14.45% of relative error) between the MP2(full)/6-311++G** and MP2(fc)/6-311++G** method. For Li(+) cation, the complexation is mainly energetically stabilized by the lower rim/cation (namely O-Li(+)) interaction. However, binding energies and NBO analyses confirm that Na(+) cation prefers to enter the calix[4]arene cavity and the cation-pi interaction is predominant, which contradicts the previous low-level theoretical studies. Furthermore, the complexation with Li(+) is preferred over that with Na(+) by at least 12.70 kJ mol(-1) at MP2(full)/6-311++G**//B3LYP/6-311++G** level.

Rotational excitation and de-excitation of C2(X Σ1g+) by para-H2(j=)

For the van der Waals C(2)(X (1)Sigma(g)(+))-H(2) molecular system, we generated a new ab initio potential energy surface (PES). We mapped this PES at the multireference internally contracted configuration-interaction method including the Davidson correction together with a large diffuse basis set. Then, we incorporated our PES into quantum scattering calculations at the close coupling and infinite order sudden approximation methods to cover collision energies ranging from 0.1 up to 4000 cm(-1). After Boltzmann thermal averaging, rate coefficients for temperatures of up to 1000 K are deduced. Discrepancies between our new rates and those computed previously are noticed. This should induce deviations in astrophysical modeling.

Modeling temporary anions in density functional theory: Calculation of the Fukui function

Two approaches are investigated for modeling electron densities of temporary anions in density functional theory (DFT). Both rely on an artificial binding of the excess electron, in one case by a compact basis set and in the other by a potential wall. The key feature of the calculations is that the degree of binding is controlled in both cases by knowledge of the negative electron affinity of the corresponding neutral, approximated in terms of DFT local functional frontier orbital eigenvalues and vertical ionization potential, A=-(epsilon(LUMO)+epsilon(HOMO))-I. To illustrate the two approaches, Fukui functions for nucleophilic attack are determined in four molecules with increasingly negative electron affinities. They yield very similar results, which are notably different to those determined without artificial electron binding. The use of a potential wall has the attractive feature that large, diffuse basis sets can be used, avoiding the need for a compact basis, tailored to a particular molecule.

Accuracy of distributed multipoles and polarizabilities: Comparison between the LoProp and MpProp models

Localized multipole moments up to the fifth moment as well as localized dipole polarizabilities are calculated with the MpProp and the newly developed LoProp methods for a total of 20 molecules, predominantly derived from amino acids. A comparison of electrostatic potentials calculated from the multipole expansion obtained by the two methods with ab initio results shows that both methods reproduce the electrostatic interaction with an elementary charge with a mean absolute error of approximately 1.5 kJ/mol at contact distance and less than 0.1 kJ/mol at distances 2 A further out when terms up to the octupole moments are included. The polarizabilities are tested with homogenous electric fields and are found to have similar accuracy. The MpProp method gives better multipole moments unless diffuse basis sets are used, whereas LoProp gives better polarizabilities.

On the position of the potential wall in DFT temporary anion calculations

A simple method was recently proposed [D. J. Tozer and F. De Proft, J. Chem. Phys., 2007, 127, 034108] for performing explicit density functional theory (DFT) calculations on temporary anions. The excess electron in the anion is bound by a potential wall, the position of which is determined by a single parameter lambda, chosen to reproduce an approximate, theoretical negative electron affinity in the corresponding neutral. In the present study, the system-dependence of lambda and the sensitivity of the negative affinities to this parameter are investigated for 34 organic molecules. The results demonstrate that the system-dependent lambda values can be replaced by a global, average value, with minimal effect on the affinities. It follows that the orbitals, electron density, and other properties of a temporary anion can be determined from a single DFT calculation on that anion, using a large, diffuse basis set. As an illustration, singly occupied molecular orbitals and spin densities are determined for the anions of guanine and adenine nucleobases. Despite the use of a diffuse basis set, the method yields quantities that are localised in the molecular framework, associated with vertical electron affinities of -1.2 eV and -0.8 eV, respectively.

Comparative study of perturbative methods for computing electron transfer tunneling matrix elements with a nonorthogonal basis set

The authors consider the problem of computing tunneling matrix elements for bridge-mediated electron transfer reactions using the Lowdin [J. Math. Phys. 3, 969 (1962); J. Mol. Spectrosc. 13, 326 (1964)] projection-iteration technique with a nonorthogonal basis set. They compare the convergence properties of two different Lowdin projections, one containing the overlap matrix S and the other containing the inverse S-1 in the projected Hamiltonian. It was suggested in the literature that the projected Hamiltonian with S-1 has better convergence properties compared to the projected Hamiltonian with S. The authors test this proposal using a simple analytical model, and ab initio Hartree-Fock calculations on different molecules with several types of basis sets. Their calculations show that, for Gaussian-type basis sets, the projected Hamiltonian containing S has the best convergence properties, especially for diffuse basis sets and in the strong coupling limit. The limit of diffuse basis sets is relevant to tunneling matrix element calculations involving excited states and anionic electron transfer.

Origin invariant approaches to the calculation of two-photon circular dichroism

The origin dependence of the expression of two-photon circular dichroism in the length formulation employed by the authors in a recent computational study [B. Jansik et al., Chem. Phys. Lett. 414, 461 (2005)] is discussed in detail, and some inherently origin invariant alternative formulations are introduced. Extensive computational tests on a small reference chiral system, namely, a chiral form of H(2)O(2), are performed at the density functional theory (DFT)/B3LYP level of theory with large diffuse correlation consistent basis sets. The results indicate that the velocity formulation originally proposed by Tinoco, Jr. [J. Chem. Phys. 62, 1006 (1975)] provides the most convenient approach for an origin invariant calculation of two-photon circular dichroism.

Orientation of molecules by magnetic field as a new source of information on their structures

A complex procedure for quantitative allowance for small but significant effects of molecular orientation by strong static magnetic fields was elaborated. A series of high-resolution 1H NMR spectra of 1,2,3-trichloronaphthalene recorded at magnetic field strength varied over a wide range was analyzed in the framework of a unified approach with high accuracy. The spin-spin coupling constants and the dipole-dipole coupling constants for all pairs of 1H nuclei and the anisotropy and rhombicity parameters of the magnetic susceptibility tensor of the molecule were determined. Ab initio CSGT/RHF quantum chemical calculations of this property using a wide range of conventional diffuse and polarization basis set functions were carried out. Augmentation of the basis set with polarization functions affects the values of the calculated parameters to a lesser extent compared to augmentation with diffuse functions. The results of calculations using the 6-311G(df) and 6-311++G(df) basis sets are in good agreement with the experimental values of the magnetic susceptibility anisotropy for 1,2,3-trichloronaphthalene. The advantages of the method proposed and specific features of the effects of orientation by magnetic field as a new source of information on the structure of molecules in solution are discussed.