Double-zeta Basis Research Articles

Symmetry breaking in the cyclic C3C2H radical

We have employed high-level coupled cluster methods including connected triple excitations to study the possibility of symmetry-breaking in the (2)B(2) ground state of the c-C(3)C(2)H radical. Specifically, we find that spin-restricted open-shell Hartree-Fock (ROHF) reference orbitals yield a C(2v) structure, whereas spin-unrestricted Hartree-Fock (UHF) and Brueckner orbitals lead to a symmetry-broken C(s) minimum-energy geometry. Equation-of-motion coupled cluster singles and doubles method for ionized states yields a C(s) structure with a double-zeta basis set, but not with a triple-zeta basis set. Through a detailed analysis of the orbital instability/near-instability behavior of each type of Hartree-Fock reference, we have determined that the UHF reference wave function is more reliable than the ROHF reference in this case and that the Born-Oppenheimer potential surface for c-C(3)C(2)H exhibits a symmetry broken C(s) global minimum. This result is supported by excited-state computations, which indicate that a second-order (pseudo) Jahn-Teller interaction is responsible for the symmetry-breaking.

A DFT and ab Initio Benchmarking Study of Metal−Alkane Interactions and the Activation of Carbon−Hydrogen Bonds

Density functional theory and ab initio methods have been used to calculate the structures and energies of minima and transition states for the reactions of methane coordinated to a transition metal. The reactions studied are reversible C-H bond activation of the coordinated methane ligand to form a transition metal methyl hydride complex and dissociation of the coordinated methane ligand. The reaction sequence can be summarized as L(x)M(CH(3))H <==> L(x)M(CH(4)) <==> L(x)M + CH(4), where L(x)M is the osmium-containing fragment (C(5)H(5))Os(R(2)PCH(2)PR(2))(+) and R is H or CH(3). Three-center metal-carbon-hydrogen interactions play an important role in this system. Both basis sets and functionals have been benchmarked in this work, including new correlation consistent basis sets for a third transition series element, osmium. Double zeta quality correlation consistent basis sets yield energies close to those from calculations with quadruple-zeta basis sets, with variations that are smaller than the differences between functionals. The energies of important species on the potential energy surface, calculated by using 10 DFT functionals, are compared both to experimental values and to CCSD(T) single point calculations. Kohn-Sham natural bond orbital descriptions are used to understand the differences between functionals. Older functionals favor electrostatic interactions over weak donor-acceptor interactions and, therefore, are not particularly well suited for describing systems--such as sigma-complexes--in which the latter are dominant. Newer kinetic and dispersion-corrected functionals such as MPW1K and M05-2X provide significantly better descriptions of the bonding interactions, as judged by their ability to predict energies closer to CCSD(T) values. Kohn-Sham and natural bond orbitals are used to differentiate between bonding descriptions. Our evaluations of these basis sets and DFT functionals lead us to recommend the use of dispersion corrected functionals in conjunction with double-zeta or larger basis sets with polarization functions for calculations involving weak interactions, such as those found in sigma-complexes with transition metals.

Revised relativistic basis sets for the 5d elements Hf–Hg

The relativistic double-zeta (dz) and triple-zeta (tz) basis sets for the 5d elements Hf-Hg have been revised for consistency with the recently optimized 4f basis sets. The new dz basis sets have 24 s functions instead of 22 s functions, and the new tz basis sets have 30 s functions instead of 29 s functions. New contraction patterns have been determined, including the 6p orbital.

An ab initio quantum mechanical charge field molecular dynamics simulation of a dilute aqueous HCl solution

An ab initio quantum mechanical charge field (QMCF) molecular dynamics simulation has been performed to study the structural and dynamical properties of a dilute aqueous HCl solution. The solute molecule HCl and its surrounding water molecules were treated at Hartree-Fock level in conjunction with Dunning double-zeta plus polarization function basis sets. The simulation predicts an average H-Cl bond distance of 1.28 A, which is in good agreement with the experimental value. The H(HCl)...O(w) and Cl(HCl)...H(w) distances of 1.84 and 3.51 A were found for the first hydration shell. At the hydrogen site of HCl, a single water molecule is the most preferred coordination, whereas an average coordination number of 12 water molecules of the full first shell was observed for the chloride site. The hydrogen bonding at the hydrogen site of HCl is weakened by proton transfer reactions and an associated lability of ligand binding. Two proton transfer processes were observed in the QMCF MD simulation, demonstrating acid dissociation of HCl. A weak structure-making/breaking effect of HCl in water is recognized from the mean residence times of 2.1 and 0.8 ps for ligands in the neighborhood of Cl and H sites of HCl, respectively.

Accurate Calculations of Intermolecular Interaction Energies Using Explicitly Correlated Coupled Cluster Wave Functions and a Dispersion-Weighted MP2 Method

Explicitly correlated coupled-cluster calculations of intermolecular interaction energies for the S22 benchmark set of Jurecka, Sponer, Cerny, and Hobza (Chem. Phys. Phys. Chem. 2006, 8, 1985) are presented. Results obtained with the recently proposed CCSD(T)-F12a method and augmented double-zeta basis sets are found to be in very close agreement with basis set extrapolated conventional CCSD(T) results. Furthermore, we propose a dispersion-weighted MP2 (DW-MP2) approximation that combines the good accuracy of MP2 for complexes with predominately electrostatic bonding and SCS-MP2 for dispersion-dominated ones. The MP2-F12 and SCS-MP2-F12 correlation energies are weighted by a switching function that depends on the relative HF and correlation contributions to the interaction energy. For the S22 set, this yields a mean absolute deviation of 0.2 kcal/mol from the CCSD(T)-F12a results. The method, which allows obtaining accurate results at low cost, is also tested for a number of dimers that are not in the training set.

Variational determination of the second-order density matrix for the isoelectronic series of beryllium, neon, and silicon

The isoelectronic series of Be, Ne, and Si are investigated using a variational determination of the second-order density matrix. A semidefinite program was developed that exploits all rotational and spin symmetries in the atomic system. We find that the method is capable of describing the strong static electron correlations due to the incipient degeneracy in the hydrogenic spectrum for increasing central charge. Apart from the ground-state energy, various other properties are extracted from the variationally determined second-order density matrix. The ionization energy is constructed using the extended Koopmans' theorem. The natural occupations are also studied, as well as the correlated Hartree-Fock-like single-particle energies. The exploitation of symmetry allows to study the basis set dependence and results are presented for correlation-consistent polarized valence double, triple, and quadruple zeta basis sets.

The Accuracy of Geometries for Iron Porphyrin Complexes from Density Functional Theory

Iron porphyrin complexes are cofactors in many important proteins such as cytochromes P450, hemoglobin, heme peroxidases, etc. Many computational studies on these systems have been done over the past decade. In this study, the performance of some of the most commonly used density functional theory functionals is evaluated with regard to how they reproduce experimental structures. Seven different functionals (BP86, PBE, PBE0, TPSS, TPSSH, B3LYP, and B97-D) are used to study eight different iron porphyrin complexes. The results show that the TPSSH, PBE0, and TPSS functionals give the best results (absolute bond distance deviations of 0.015-0.016 A), but the geometries are well-reproduced by all functionals except B3LYP. We also test four different basis sets of double-zeta quality, and we find that a combination of double-zeta basis set of Schafer et al. on the iron atom and the 6-31G* basis set on the other atoms performs best. Finally, we remove the porphyrin side chains and increase the basis set size systematically to see if this affects the results. We show that basis sets larger than double-zeta quality are not necessary to get accurate geometries, and nonaromatic side chains do not affect the geometries.

Ab initio surfaces of singlet and triplet methylene

Ab initio minimum energy hypersurfaces of singlet and triplet methylene (CH2) are examined using SCSCF. SCSCF + CI, and MCSCF methods with a double-zeta plus polarization basis.

Catching CO2 in a Bowl

Increased concentrations of CO(2) in the atmosphere contribute to global climate change. Improved methods are needed for removing CO(2) from the flue gas of power plants and/or directly from the atmosphere. A macrocyclic amidourea recently synthesized by Brooks et al., when dissolved in DMSO along with tetrabutyl ammonium fluoride, removes CO(2) from the atmosphere to form a complex in which a CO(3) group is held by a number of O-H-N bonds within the bowl-shaped cavity of the macrocycle. We have calculated the structure, stability, and vibrational spectra of this complex, using density functional techniques and polarized double-zeta basis sets. Both basis set superposition errors and polarizable continuum effects on the complex geometry and stability have been evaluated. The calculated structure is in good agreement with experiment. We predict that this CO(3)(-2) complex (and its HCO(3)(-) analogue) have larger formation constants by several orders of magnitude than the analogue complex of the amidourea macrocycle with Cl(-) (particularly in DMSO solution compared to aqueous solution). Our calculations also indicate that the CO(3)(-2) and HCO(3)(-) complexes can be distinguished by (13)C NMR. The CO(3)(-2) complex also has a distinctive H-N stretch, perturbed by the H-bonding to the CO(3) group. We also calculate the CO(3)(-2) complex to absorb within the visible region, unlike the free macrocycle or typical metal carbonates. Macrocycles of this type may provide a useful route to the absorption of atmospheric CO(2). Our calculations also indicate that changing the solvent from DMSO to water and/or heating the complex will be an efficient way to decompose it to release CO(2).

Localized orbitals in the coupled cluster singles and doubles model

In the vast majority of many-body perturbation theory and coupled-cluster method (MBPT/CCM) calculations, the self-consistent field (SCF) wavefunction is employed as the zeroth-order wave-function, and its associated canonical orbitals as the molecular orbital basis. The recent development of the coupled-cluster singles and doubles (CCSD) formalism provides an opportunity to explore alternative reference function and orbital choices, on a consistent basis. Here we examine, specifically, sets of orbitals that are more “localized” than the SCF orbitals. In particular, the bonding orbitals are selected to resemble traditional chemical bonds. CCSD calculations in the localized basis on methane employing a better than double-zeta basis set are performed and compared with conventional SCF basis results.

Simulated ab initio molecular orbital methods for polymers

The simulated ab initio molecular orbital method for polymers is described and analyzed in detail. It is shown that the approximations inherent in the method have their counterpart in the fully ab initio technique. The model systems of (BeH2)n and (CH2)n are studied in detail using several differently sized pattern molecules as data. The method is extended to the use of double-zeta basis sets for the first time. Results appear to be as accurate as ab initio results at considerably greater economy.

Density functional theory study of the mechanism for Ni(NHC) 2 catalyzed dehydrogenation of ammonia–borane for chemical hydrogen storage

The mechanism for catalytic dehydrogenation of ammonia–borane (AB = H 3N–BH 3), a promising candidate for chemical hydrogen storage, by the Ni(NHC) 2 complexes was studied by using density functional theory at the non-empirical meta-GGA level, Tao–Perdew–Staroverov–Scuseria (TPSS) functional, with all-electron correlation-consistent polarized valence double-zeta (cc-pVDZ) basis set. The mechanism for both the first and the second H 2 release from AB was studied for the first time. Several unusual aspects of this catalytic mechanism were revealed through our calculations. First, the first H 2 release begins with proton transfer from nitrogen to the Ni bound carbene carbon, forming a new C–H bond, instead of the previously hypothesized direct B–H or N–H bond activation. Second, this new C–H bond is activated by the metal, transferring the H to Ni, then forming the H 2 molecule by transferring another H from B to Ni, rather than β-H transfer. Third, the second H 2 release from H 2N–BH 2 begins with the breaking of a 3-center, 2-electron Ni–H–B bridging structure with the assistance of the unsaturated carbene carbon atom to form a B–C bond. Fourth, a nearly rhombic N 2B 2H 6 structure is formed to help the regeneration of the catalyst Ni(NHC) 2. These reaction pathways explain the importance of NHC ligands in this catalytic process and yield lower energy barriers than those mechanisms that begin with N–H or B–H activations catalyzed by the metal atoms. The predicted reaction mechanism which features unexpected ligand participation points the way to finding new catalysts with higher efficiency, as partial unsaturation of the M–L bond may be essential for low energy H transfers.

Mechanism of the Catalytic Activity of Nucleophiles in the Stepwise Hydrolysis and Condensation Reactions of Tetramethoxysilane

Active ingredients: A model for the simplest hydrolysis reaction is applied to all stages of stepwise hydrolysis and condensation taking place during a sol-gel process. The picture shows the molecular structures of the transition states of the ammonia- (left) and OH(-)-promoted (right) condensation reactions of two Si(OH)(4) molecules, including an additional water molecule.The previously proposed model of the catalytic activity of nucleophiles in the hydrolysis reaction of tetramethoxysilane is expanded to the subsequent stages of hydrolysis, that is, the stepwise hydrolysis of (MeO)(4-x)(OH)(x)Si (x=1-3) molecules, and to the condensation reaction of completely hydrolysed species. The estimate of the reaction barrier heights by using the B3LYP and MP2 methods with correlation-consistent double-zeta basis sets allows us to predict the catalytic activity of bases for the different steps of hydrolysis and for condensation reactions. In general, the catalytic activity of bases decreases with the number of hydrolysed groups, vanishing in the case of ammonia at x=2 and remaining in the case of the hydroxyl anion up to x=3. In addition, the value of the catalytic activity of NH(3) and OH(-) is of the same order of magnitude for hydrolysis reactions, while the effect of the OH(-) anion substantially exceeds that of NH(3) for condensation reactions.

Photocatalytic oxidation of dinitronaphthalenes: Theory and experiment

A combination of photocatalytic oxidation experiments and quantum mechanical calculations was used in order to describe the mechanism and the nature of the photocatalytic oxidation reactions of dinitronaphthalane isomers and interprete their reactivities within the framework of the Density Functional Theory (DFT). The photocatalytic oxidation reactions of three dinitronaphthalene isomers, 1,3-dinitronaphthalene, 1,5-dinitronaphthalene and 1,8-dinitronaphthalene in the presence of TiO 2 Degussa P-25 grade were investigated experimentally. The reactions were carried out in a Solarbox photoreactor equipped with a Xenon lamp. The removal of the individual substrates was followed by means of a gas chromatographic method. Nonpurgable organic carbon contents of the samples were determined by means of the catalytic oxidation method using Total Organic Carbon analyzer. With the intention of determining the best reactivity descriptors to explain the differences in the photocatalytic oxidation rates in terms of the molecular properties, geometry optimizations of the compounds were performed with the Density Functional Theory DFT at B3LYP/6-31G ∗ level. In order to take the effect of adsorption on the oxidation rate, a cluster Ti 9O 18 cut from the anatase bulk structure was modeled. The binding energies for the compounds were calculated by using the double-zeta basis set. Global hardness, softness, Fukui functions, local hardness–softness and local softness differences were calculated. The results show that the reactions investigated are orbital-controlled and electrophilic in nature. Local DFT descriptors reflect the reactivities of the dinitronaphthalene isomers better than the global ones, due to the differences in their adsorptive capacities.

An ab initio molecular orbital study of the nuclear volume effects in uranium isotope fractionations

This paper discusses the nuclear volume dependence of uranium isotope fractionations in the U(3+)-U(4+) and U(4+)-UO(2) (2+) systems by reference to a series of ab initio molecular orbital calculations. Nuclear volume-dependent terms ( identical withln K(nv)) in isotope fractionation coefficients ( identical withepsilon) are calculated from the energetic balance of the isotopomers involved in the systems. We used the Dirac-Coulomb Hartree-Fock (DCHF) method with the Gaussian-type finite-nucleus model. We employed three types of generally contracted Gaussian basis sets to check the basis set dependences. In the U(3+)-U(4+) system, the present values of ln K(nv) for uranium, other than those with the smallest double-zeta basis set, are in good agreement with previous values of ln K(nv) obtained from a numerical atomic multiconfigurational DCHF method with the Fermi-type finite-nucleus model. The present calculations reasonably reproduce the experimental value of epsilon in the U(3+)-U(4+) system, and the value of ln K(nv) in the U(4+)-UO(2) (2+) system, obtained empirically by temperature-dependent fitting of the experimental epsilon values. For instance, in the U(4+)-UO(2) (2+) system, the present ab initio ln K(nv) value for a (235)U-(238)U isotope pair is 0.002 09 using the largest basis set, while the experimental value is 0.002 24. This paper also shows that nuclear volume effects are negligibly small on the U-O bond length and two force constants of UO(2) (2+). Hence, the molecular vibrational terms of the isotope fractionation coefficients mainly depend on the nuclear mass rather than the nuclear volume.

Comprehensive Study on the Solvation of Mono- and Divalent Metal Cations: Li+, Na+, K+, Be2+, Mg2+ and Ca2+

Hydration of mono- and divalent metal ions (Li(+), Na(+), K(+), Be(2+), Mg(2+) and Ca(2+)) has been studied using the DFT (B3LYP), second-order Møller-Plesset (MP2) and CCSD(T) perturbation theory as well as the G3 quantum chemical methods. Double-zeta and triple-zeta basis sets containing both (multiple) polarization and diffuse functions were applied. Total and sequential binding energies are evaluated for all metal-water clusters containing 1-6 water molecules. Total binding energies predicted at lower levels of theory are compared with those from the high level G3 calculations, whereas the sequential binding energies are compared with available experimental values. An increase in the quality of the basis set from double-zeta to triple-zeta has a significant effect on the sequential binding energies, irrespective of the geometries used. Within the same group (I or II), the sequential binding energy predictions at the MP2 and B3LYP vary appreciably. We noticed that, for each addition of a water molecule, the change of the M-O distance in metal-water clusters is higher at the B3LYP than at the MP2 level. The charge of the metal ion decreases monotonically as the number of water molecules increase in the complex.

Gaussian basis set of double zeta quality for atoms K through Kr: Application in DFT calculations of molecular properties

Contracted basis sets of double zeta (DZ) quality for the atoms from K to Kr are presented. They were determined from fully optimized basis sets of primitive Gaussian-type functions generated in atomic Hartree-Fock calculations. Sets of Gaussian polarization functions optimized at the Möller-Plesset second-order level were added to the DZ basis set. This extends earlier work on segmented contracted DZ basis set for atoms H-Ar. From this set, using the BP86 nonhybrid and B3LYP hybrid functionals, dissociation energy, geometric parameters, harmonic vibrational frequency, and electric dipole moment of a set of molecules were calculated and compared with results obtained with other basis sets and with experimental data reported in the literature. In addition, (57)Fe and (77)Se nuclear magnetic resonance chemical shifts in Fe(C(5)H(5))(2), H(2)Se, and CSe(2) were calculated using density functional theory and gauge-including atomic orbitals and, then, compared with theoretical and experimental values previously published in the literature. Except for chemical shift, one verifies that our results give the best agreement with experimental and benchmark values.

The accuracy of local MP2 methods for conformational energies

The relative energies of 95 conformers of four peptide models are studied using MP2 and LMP2 methods and correlation consistent basis sets ranging from double-zeta to augmented quintuple-zeta quality. It is found that both methods yield quite similar results, and the differences between MP2 and LMP2 decrease systematically with increasing basis set. Due to reduced intramolecular basis set superposition effects (BSSE), the LMP2 results converge more slowly to the basis set limit for most of these rather small systems. However, for larger peptides, the BSSE has a very large effect on the energy difference between extended and helical structures, leading to a very strong basis set dependence of the canonical MP2 results. It is demonstrated for alanine octapeptides that the basis set error exceeds 30 and 20kJ mol−1, respectively, if augmented double-zeta and triple-zeta basis sets are used. On the other hand, the LMP2 results are only slightly affected by the basis set size, and, even with augmented double-zeta basis sets, reasonably accurate results are obtained. Furthermore, for the larger systems, the computation times for the LMP2 calculations are shown to be up to one order or magnitude shorter than for canonical MP2 calculations with the same basis set.

The possibility of the decomposition of 2′‐deoxyribose moiety of thymidine induced by the low energy electron attachment

To evaluate the possibility of the decomposition of 2-deoxyribose moiety of thymidine induced by low energy electrons (LEE) attachment, the transition states and the energy barriers of the bond breaking processes of the ribose of the nucleoside have been studied theoretically by applying the density functional theory with the double zeta basis sets (DZP++). The energy barriers for the breakage of the C-C bonds (C(1')-C(2'), C(2')-C(3'), C(3')-C(4'), and C(4')-C(5')) of the ribose group of the radical anion of thymidine are found to be high (ca. 42-57 kcal/mol). The total energies of the C-C bond-broken products are significantly higher than that of the radical anion dT(*-). The decomposition of dT(*-) through the C-C bond rupture is unlikely to take place. The rupture of the C(1')-O(4') bond of dT(*-) needs an activation energy as low as 10.4 kcal/mol. However, the reversed reaction (C(1')-O(4') bond formation) needs the activation energy low as 0.3 kcal/mol. Therefore, the intermediate product LM1(C1')-(O4') is unlikely to be stable and the C(1')-O(4') bond-broken is not favored. The activation energy of the C(4')-O(4') bond rupture process amounts to 20.5 kcal/mol. The total energy of the C(4')-O(4') bond broken product is about 6.5 kcal/mol lower than that of the reactant dT(*-). The subsequent N1-glycosidic bond breaking process is found to have a very low energy barrier. Therefore, the LEE-induced base release through the C(4')-O(4') bond rupture might be a possible pathway.

DFT Calculation of 1J(119Sn,13C) and 2J(119Sn,1H) Coupling Constants in Di- and Trimethyltin(IV) Compounds

We have tested several computational protocols, at the nonrelativistic DFT level of theory, for the calculation of 1J(119Sn, 13C) and 2J(119Sn, 1H) spin-spin coupling constants in di- and trimethyltin(IV) derivatives with various ligands. Quite a good agreement with experimental data has been found with several hybrid functionals and a double-zeta basis set for a set of molecules comprising tetra-, penta-, and hexa-coordinated tin(IV). Then, some of the protocols have been applied to the calculation of the 2J(119Sn, 1H) of the aquodimethyltin(IV) ion and dimethyltin(IV) complex with D-ribonic acid and to the calculation of 1J(119Sn, 13C) and 2J(119Sn, 1H) of the dimethyltin(IV)-glycylglycine and glycylhistidine complexes in water solutions. Solvent effects have been considered in these cases by including explicit water molecules and/or the solvent reaction field, resulting in a good agreement with experimental data. The proposed protocols constitute a helpful tool for the structural determination of di- and triorganotin(IV) derivatives.