Double-zeta Quality Basis Research Articles

Fragmentation Method for Computing Quantum Mechanics and Molecular Mechanics Gradients for Force Matching: Validation with Hydration Free Energy Predictions Using Adaptive Force Matching.

A fragmentation approach referred to as a simple overlapping region method for force matching (SORForM) is presented. SORForM is designed to enable efficient computation of quantum mechanical (QM) forces for large molecules and is validated in the framework of adaptive force matching (AFM) to develop solute models in water. The SORForM method divides a molecule into overlapping QM regions with each region containing a gradient zone and a buffer zone. The buffer zone ensures that the atoms in the gradient zone have their surroundings unchanged with fragmentation. The performance of the method is validated with mefenamic acid and linalyl acetate by comparing the hydration free energies of AFM models developed with and without SORForM. The AFM hydration free energies are also compared with that of the experiments. The models developed with B3LYP-D3(BJ) and def2-TZVP are in excellent agreement with experiments. Our work shows that PBE-D3(BJ) provides less satisfactory results when compared to B3LYP-D3(BJ). The def2-TZVP basis set is found to greatly improve the agreement with experiments when compared to a double-zeta quality basis set.

Metal-organic frameworks properties from hybrid density functional approximations.

The chemical versatility and modular nature of Metal-Organic Frameworks (MOFs) make them unique hybrid inorganic-organic materials for several important applications. From a computational point of view, ab initio modeling of MOFs is a challenging and demanding task, in particular, when the system reaches the size of gigantic MOFs as MIL-100 and MIL-101 (where MIL stands for Materials Institute Lavoisier) with several thousand atoms in the unit cell. Here, we show how such complex systems can be successfully tackled by a recently proposed class of composite electronic structure methods revised for solid-state calculations. These methods rely on HF/density functional theory hybrid functionals (i.e., PBEsol0 and HSEsol) combined with a double-zeta quality basis set. They are augmented with semi-classical corrections to take into account dispersive interactions (D3 scheme) and the basis set superposition error (gCP). The resulting methodologies, dubbed "sol-3c," are cost-effective yet reach the hybrid functional accuracy. Here, sol-3c methods are effectively applied to predict the structural, vibrational, electronic, and adsorption properties of some of the most common MOFs. Calculations are feasible even on very large MOFs containing more than 2500 atoms in the unit cell as MIL-100 and MIL-101 with reasonable computing resources. We propose to use our composite methods for the routine in silico screening of MOFs targeting properties beyond plain structural features.

Basis set convergence of CCSD(T) equilibrium geometries using a large and diverse set of molecular structures.

We examine the basis set convergence of the CCSD(T) method for obtaining the structures of the 108 neutral first- and second-row species in the W4-11 database (with up to five non-hydrogen atoms). This set includes a total of 181 unique bonds: 75 H-X, 49 X-Y, 43 X=Y, and 14 X≡Y bonds (where X and Y are first- and second-row atoms). As reference values, geometries optimized at the CCSD(T)/aug'-cc-pV(6+d)Z level of theory are used. We consider the basis set convergence of the CCSD(T) method with the correlation consistent basis sets cc-pV(n+d)Z and aug'-cc-pV(n+d)Z (n = D, T, Q, 5) and the Weigend-Ahlrichs def2-n ZVPP basis sets (n = T, Q). For each increase in the highest angular momentum present in the basis set, the root-mean-square deviation (RMSD) over the bond distances is decreased by a factor of ∼4. For example, the following RMSDs are obtained for the cc-pV(n+d)Z basis sets 0.0196 (D), 0.0050 (T), 0.0015 (Q), and 0.0004 (5) Å. Similar results are obtained for the aug'-cc-pV(n+d)Z and def2-n ZVPP basis sets. The double-zeta and triple-zeta quality basis sets systematically and significantly overestimate the bond distances. A simple and cost-effective way to improve the performance of these basis sets is to scale the bond distances by an empirical scaling factor of 0.9865 (cc-pV(D+d)Z) and 0.9969 (cc-pV(T+d)Z). This results in RMSDs of 0.0080 (scaled cc-pV(D+d)Z) and 0.0029 (scaled cc-pV(T+d)Z) Å. The basis set convergence of larger basis sets can be accelerated via standard basis-set extrapolations. In addition, the basis set convergence of explicitly correlated CCSD(T)-F12 calculations is investigated in conjunction with the cc-pVnZ-F12 basis sets (n = D, T). Typically, one "gains" two angular momenta in the explicitly correlated calculations. That is, the CCSD(T)-F12/cc-pVnZ-F12 level of theory shows similar performance to the CCSD(T)/cc-pV(n+2)Z level of theory. In particular, the following RMSDs are obtained for the cc-pVnZ-F12 basis sets 0.0019 (D) and 0.0006 (T) Å. Overall, the CCSD(T)-F12/cc-pVDZ-F12 level of theory offers a stellar price-performance ratio and we recommend using it when highly accurate reference geometries are needed (e.g., in composite ab initio theories such as W4 and HEAT).

Experimental and Computational Studies of the Mechanisms of Hydroamination/Cyclisation of Unactivated α,ω-Amino-alkenes with CCC-NHC Pincer Zr Complexes

Four new CCC-NHC pincer Zr complexes have been synthesised, characterised, and used in mechanistic studies in the hydroamination/cyclisation of unactivated amino-alkenes. These Zr pre-catalysts will cyclise a primary amino-alkene, but no reaction was observed for a secondary amino-alkene even in the presence of a primary amine. The empirical rate law, experimentally determined activation parameters, and kinetic isotope effects (KIEs) are reported. Several possible mechanisms, including amido- versus imido-insertion and concerted-insertion versus [2 + 2] cycloaddition mechanisms, were modelled computationally at the PBEPBE level of theory with double-zeta quality basis sets. The formation of a catalytically relevant imido complex via the monoamido complexes was accompanied by in situ formation of ammonium salts of the substrates. The experimental and computational data are consistent with an imido-[2 + 2] cycloaddition mechanism for the CCC-NHC pincer diamido Zr complexes that follow saturation kinetics under catalytically relevant concentrations.

Anharmonic zero point vibrational energies: Tipping the scales in accurate thermochemistry calculations?

Anharmonic zero point vibrational energies (ZPVEs) calculated using both conventional CCSD(T) and MP2 in combination with vibrational second-order perturbation theory (VPT2) are compared to explicitly correlated CCSD(T)-F12 and MP2-F12 results that utilize vibrational configuration interaction (VCI) theory for 26 molecules of varying size. Sequences of correlation consistent basis sets are used throughout. It is found that the explicitly correlated methods yield results close to the basis set limit even with double-zeta quality basis sets. In particular, the anharmonic contributions to the ZPVE are accurately recovered at just the MP2 (or MP2-F12) level of theory. Somewhat surprisingly, the best vibrational CI results agreed with the VPT2 values with a mean unsigned deviation of just 0.09 kJ/mol and a standard deviation of just 0.11 kJ/mol. The largest difference was observed for C(4)H(4)O (0.34 kJ/mol). A simplified version of the vibrational CI procedure that limited the modal expansion to at most 2-mode coupling yielded anharmonic corrections generally within about 0.1 kJ/mol of the full 3- or 4-mode results, except in the cases of C(3)H(8) and C(4)H(4)O where the contributions were underestimated by 1.3 and 0.8 kJ/mol, respectively (34% and 40%, respectively). For the molecules considered in this work, accurate anharmonic ZPVEs are most economically obtained by combining CCSD(T)-F12a/cc-pVDZ-F12 harmonic frequencies with either MP2/aug-cc-pVTZ/VPT2 or MP2-F12/cc-pVDZ-F12/VCI anharmonic corrections.

The assessment of density functionals for DNA–protein stacked and T-shaped complexes

The present work uses 129 nucleobase – amino acid CCSD(T)/CBS stacking and T-shaped interaction energies as reference data to test the ability of various density functionals with double-zeta quality basis sets, as well as some semi-empirical and molecular mechanics methods, to accurately describe noncovalent DNA–protein π–π and π+–π interactions. The goal of this work is to identify methods that can be used in hybrid approaches (QM/MM, ONIOM) for large-scale modeling of enzymatic systems involving active-site (substrate) π–π contacts. Our results indicate that AMBER is a more appropriate choice for the lower-level method in hybrid techniques than popular semi-empirical methods (AM1, PM3), and suggest that AMBER accurately describes the π–π interactions found throughout DNA–protein complexes. The M06–2X and PBE-D density functionals were found to provide very promising descriptions of the 129 nucleobase – amino acid interaction energies, which suggests that these may be the most suitable methods for describing high-level regions. Therefore, M06–2X and PBE-D with both the 6–31G(d) and 6–31+G(d,p) basis sets were further examined through potential-energy surface scans to better understand how these techniques describe DNA–protein π–π interactions in both minimum and nonminimum regions of the potential-energy surfaces, which is critical information when modeling enzymatic reaction pathways. Our results suggest that studies of stacked nucleobase – amino acid systems should implement the PBE-D/6–31+G(d,p) method. However, if T-shaped contacts are involved and (or) smaller basis sets must be considered due to limitations in computational resources, then M06–2X/6–31G(d) provides an overall excellent description of both nucleobase – amino acid stacking and T-shaped interactions for a range of DNA–protein π–π and π+–π interactions.

Assessment of the Accuracy of Shape-Consistent Relativistic Effective Core Potentials Using Multireference Spin−Orbit Configuration Interaction Singles and Doubles Calculations of the Ground and Low-Lying Excited States of U4+and U5+

Multireference spin-orbit configuration interaction calculations were used to determine the accuracy of 60-, 68-, and 78-electron shape-consistent relativistic effective core potentials (RECPs) for uranium V and VI ground and low-lying excited states. Both 5f(n) and (5f6d)(n), (n = 1, 2) reference spaces were investigated using correlation-consistent double-zeta quality basis sets. Accuracy was assessed against gas-phase experimental spectra. The 68-electron RECP calculations yielded low relative and rms errors and predicted the empirical ordering of states most consistently.

A comparative study of semiempirical, ab initio, and DFT methods in evaluating metal–ligand bond strength, proton affinity, and interactions between first and second shell ligands in Zn‐biomimetic complexes

Although theoretical methods are now available which give very accurate results, often comparable to the experimental ones, modeling chemical or biological interesting systems often requires less demanding and less accurate theoretical methods, mainly due to computer limitations. Therefore, it is crucial to know the precision of such less reliable methods for relevant models and data. This has been done in this work for small zinc-active site models including O- (H(2)O and OH(-)) and N-donor (NH(3) and imidazole) ligands. Calculations using a number of quantum mechanical methods were carried out to determine their precision for geometries, coordination number relative stability, metal-ligand bond strengths, proton affinities, and interaction energies between first and second shell ligands. We have found that obtaining chemical accuracy can be as straightforward as HF geometry optimization with a double-zeta plus polarization basis followed by a B3LYP energy calculation with a triple-zeta quality basis set including diffuse and polarization functions. The use of levels as low as PM3 geometry optimization followed by a B3LYP single-point energy calculation with a double-zeta quality basis including polarization functions already yields useful trends in bond length, proton affinities or bond dissociation energies, provided that appropriate caution is taken with the optimized structures. The reliability of these levels of calculation has been successfully demonstrated for real biomimetic cases.

Combining explicitly correlated R12 and Gaussian geminal electronic structure theories

Explicitly correlated R12 methods using a single short-range correlation factor (also known as F12 methods) have dramatically smaller basis set errors compared to the standard wave function counterparts, even when used with small basis sets. Correlations on several length scales, however, may not be described efficiently with one correlation factor. Here the authors explore a more general MP2-R12 method in which each electron pair uses a set of (contracted) Gaussian-type geminals (GTGs) with fixed exponents, whose coefficients are optimized linearly. The following features distinguish the current method from related explicitly correlated approaches published in the literature: (1) only two-electron integrals are needed, (2) the only approximations are the resolution of the identity and the generalized Brillouin condition, (3) only linear parameters are optimized, and (4) an arbitrary number of (non-)contracted GTGs can appear. The present method using only three GTGs and a double-zeta quality basis computed valence correlation energies for a set of 20 small molecules only 2.2% removed from the basis set limit. The average basis set error reduces to 1.2% using a near-complete set of seven GTGs with the double-zeta basis set. The conventional MP2 energies computed with much larger quadruple, quintuple, and sextuple basis sets all had larger average errors: 4.6%, 2.4%, and 1.5%, respectively. The new method compares well to the published MP2-R12 method using a single Slater-type geminal (STG) correlation factor. For example, the average basis set error in the absolute MP2-R12 energy obtained with the exp(-r12) correlation factor is 1.7%. Correlation contribution to atomization energies evaluated with the present method and with the STG-based method only required a double-zeta basis set to exceed the precision of the conventional sextuple-zeta result. The new method is shown to always be numerically stable if linear dependencies are removed from the two-particle basis and the zeroth-order Hamiltonian matrix is made positive definite.

On the performance of the intermediate Hamiltonian Fock-space coupled-cluster method on linear triatomic molecules: The electronic spectra of NpO2+, NpO22+, and PuO22+

In this paper we explore the use of the novel relativistic intermediate Hamiltonian Fock-space coupled-cluster method in the calculation of the electronic spectrum for small actinyl ions (NpO2+, NpO2(2+), and PuO2(2+)). It is established that the method, in combination with uncontracted double-zeta quality basis sets, yields excitation energies in good agreement with experimental values, and better than those obtained previously with other theoretical methods. We propose the reassignment of some of the peaks that were observed experimentally, and confirm other assignments.

Carbon monoxide adsorption on alkali and proton-exchanged chabazite: an ab-initio periodic study using the CRYSTAL code

Ab initio periodic calculations based on local Gaussian basis sets as coded in the CRYSTAL program have been performed to investigate the structure, the binding energy and the vibrational features of carbon monoxide adsorbed on H+, Li+, Na+ and K+-exchanged chabazite (Si/Al = 11/1, i.e. one Al atom per unit cell). The hybrid B3LYP functional has been adopted for all calculations with a polarized double-zeta quality basis set. The B3LYP binding energies (BSSE corrected) are 16.0, 24.6, 20.4 and 5.1 kJ/mol for H+, Li+, Na+ and K+-exchanged chabazite, respectively. Corresponding CO hypsochromic stretching frequency shifts are 47, 68, 43 and 33 cm−1, respectively. Comparison with the case of CO interacting with bare alkali cations and the available experimental data on a variety of zeolites has also been addressed.

Multiconfiguration self-consistent-field theory based upon the fragment molecular orbital method

The fragment molecular orbital (FMO) method was combined with the multiconfiguration self-consistent-field (MCSCF) theory. One- and two-layer approaches were developed, the former involving all dimer MCSCF calculations and the latter limiting MCSCF calculations to a small part of the system. The accuracy of the two methods was tested using the six electrons in six orbitals complete active space type of MCSCF and singlet spin state for phenol+(H(2)O)(n), n=16,32,64 (6-31G( *) and 6-311G( *) basis sets); alpha helices and beta strands of phenylalanine-(alanine)(n), n=4,8,16 (6-31G( *)). Both double-zeta and triple-zeta quality basis sets with polarization were found to have very similar accuracy. The error in the correlation energy was at most 0.000 88 a.u., the error in the gradient of the correlation energy was at most 6.x10(-5) a.u./bohr and the error in the correlation correction to the dipole moment was at most 0.018 D. In addition, vertical singlet-triplet electron excitation energies were computed for phenol+(H(2)O)(n), (n=16,32,64), 6-31G( *), and the errors were found to be at most 0.02 eV. Approximately linear scaling was observed for the FMO-based MCSCF methods. As an example, an FMO-based MCSCF calculation with 1262 basis functions took 98 min on one 3.0 GHz Pentium4 node with 1 Gbyte RAM.

Ab initio study of AmCl(+): f-f spectroscopy and chemical binding.

A valence full configuration interaction study with a polarized double-zeta quality basis set has been carried out for the lowest 49 electronic states of AmCl(+). The calculations use a pseudopotential treatment for the core electrons and incorporate a one-electron spin-orbit interaction operator. Electrons in the valence s, p, d, and f subshells were included in the active space. The resulting electronic potential energy curves are largely repulsive. The chemical bonding is ionic in character with negligible participation of 5f electrons. The molecular f-f spectroscopy of AmCl(+) arises essentially from an in situ Am(2+) core with states slightly redshifted by the presence of chloride ion. Am(+)+Cl asymptotes which give rise to the few attractive potential energy curves can be predicted by analysis of the f-f spectroscopy of isolated Am(+) and Am(2+). The attractive curves have substantial binding energies, on the order of 75-80 kcal/mol, and are noticeably lower than recent indirect measurements on the isovalent EuCl(+). An independent empirical correlation supports the predicted reduction in AmCl(+) binding energy. The energies of the repulsive curves are strongly dependent on the selection of the underlying atomic orbitals while the energies of the attractive curves do not display this sensitivity. The calculations were carried out using our recently developed parallel spin-orbit configuration interaction software.

A computational investigation on the mechanism of the reaction between O( 1D) and NF 3

The mechanism of the reaction between O( 1 D) and NF 3, experimentally studied by spectroscopic techniques [V.I. Sorokin, N.P. Gritsan, A.I. Chichinin, J. Chem. Phys. 108 (1998) 8995], has been investigated at the Coupled Cluster level of theory in conjunction with double-zeta and triple-zeta quality basis sets. The process commences by the exoergic (105.4 kcal mol −1 ) formation, on the singlet surface, of the O–NF 3 intermediate, whose eventual dissociation into NF 2 and OF passes through the isomerization to F 2N–OF. The energy barrier of this process, 58.8 kcal mol −1 , is significantly lower than the intersystem crossing from the singlet O–NF 3 to the triplet O( 3 P) and NF 3 dissociation products. This is consistent with the experimental observation that, in the reaction between O( 1 D) and NF 3, the unreactive quenching to O( 3 P) represents only a minor reaction channel.

An ab initio study of the ionization potentials and f–f spectroscopy of europium atoms and ions

The first three ionization potentials of europium and the f–f spectroscopy of the two lowest multiplets of Eu+3 have been calculated using ab initio spin–orbit configuration interaction techniques. To accomplish this, a new averaged relativistic effective core potential has been developed which leaves only the 5s, 5p, and 4f in the valence space. A series of configuration interaction calculations were carried out up through single and partial double excitations with a double-zeta quality basis set. The computed ionization values have an absolute error of about 0.1 eV from the experimental values. The computed f–f spectroscopy for the lowest F7 multiplet of Eu+3 has a RMS error with experiment of about 100 cm−1. The computed f–f spectroscopy for the first excited D5 multiplet has a higher RMS error of about 350 cm−1. The computed center of gravity separation between the D5–F7 multiplet is underestimated by 750 cm−1. Comparisons between non-spin–orbit and spin–orbit configuration interaction calculations for the separations of the centers of gravity of multiplets are very favorable up through single and double excitations with differences of a tenth of an eV or less. The spin–orbit configuration interaction calculations are among the largest ever performed for lanthanides, with expansion lengths in excess of 1.9 million double-group-adapted functions. The calculations were achieved by application of a new parallel spin–orbit configuration interaction component in the COLUMBUS Program System.

Ring, chain, and cluster compounds in the Cl-Ga-N-H system.

The formation of gas-phase oligomer compounds in the Cl-Ga-N-H system is considered using hybrid Hartree-Fock/density functional theory and a polarized double-zeta quality basis set. Geometric parameters, vibrational frequencies, and thermodynamic characteristics for the Cl(3)GaNH(3) adduct, its dissociation products GaCl(n), NH(n), (n= 1-3), the amidochlorogallanes [Cl(2)GaNH(2)](n) (n = 1-3), their donor-acceptor complexes with GaCl(3) and NH(3), and the imidochlorogallanes [ClGaNH](n) (n = 1-4,6) have been obtained. Generation of amidochlorogallanes is expected to be viable during laser assisted chemical vapor deposition (CVD) at low temperatures. High-temperature association processes in the gas phase during the CVD of GaN from the Cl(3)GaNH(3) adduct are predicted to be less important, in contrast to previous findings for the aluminum analogue. This difference may be explained in terms of a much lower Ga-N bond energy compared to Al-N in the ring and cluster compounds.

Relative stability of 1C 4 and 4C 1 chair forms of β- d-glucose: a density functional study

The method and basis set dependence of the relative energies of the 1C 4 and 4C 1 chair forms of β- d-glucose were calculated for two selected, low-energy hydroxyl rotamers at various levels of generalized gradient approximation density functional theory (GGA-DFT). The GGA-DFT and MP2 methods provide similar energetic differences for β- d-glucose conformers. Addition of the diffuse functions to a double-zeta quality basis set and inclusion of the HF exchange into the DFT functionals improve the agreement between the DFT and the best composite estimates of the energetic differences. The GGA- or hybrid-DFT methods reproduce the geometrical consequences of correlation effects correctly for glucose.

Second-order perturbation theory using correlated orbitals. II. A coupled MCSCF perturbation strategy for electronic spectra and its applications to ethylene, formaldehyde and vinylidene

Abstract In this second paper, the philosophy of coupling multiconfigurational variational wave functions to perturbation treatments (MC/P methodology) is extended to the calculation of electronic spectra. The corresponding methodology is presented with emphasis on its flexibility and an overview of other available approaches is given. The contracted MC/P scheme is then applied to ethylene H 2 CCH 2 , formaldehyde H 2 CO vinylidene H 2 CC. It is shown that combining well-designed averaged zeroth-order MCSCF wave functions to a barycentric Moller-Plesset (BMP) partition of the electronic Hamiltonian provides accurate spectra, contrary to Epstein-Nesbet partitions. The MC/BMP transition energies compare with experimental data within a few hundreds of cm −1 . These results have been obtained using a polarized double-zeta quality basis set augmented by a set of semi-diffuse functions (6–31 + G ∗ ) and by an extra set of diffuse orbitals to account for Rydberg states. Since non-dynamic correlations effects that are important for a proper description of the manifold of the excited states of interest are included in the MCSCF zeroth-order space will all remaining correlation effects (non-dynamic and dynamic) are treated at the perturbation level, the present study lets anticipate applications of the MC/P methodology to medium size systems without much computational trouble.

Ab initio molecular-cluster modeling of a paramagnetic excess-electron vacancy center in paratellurite

Abstract An excess-electron point defect associated with an oxygen vacancy as observed in paratellurite has been modeled and studied using the ab initio RHF-SCF molecular orbital method of the Many ELectron Description (MELD) program package. Open-shell electronic structure calculations for obtaining spin densities were performed on molecular clusters Te2O6H6 having paratellurite geometry and terminated by hydrogen-like atoms with optimized nuclear charges and O-H distances. Hyperfine and superhyperfine matrix elements were calculated based on the spin densities of the ab initio results, and the effects of spin delocalization, second-order perturbation magnetic contributions, extended CI calculations, double-zeta quality basis functions and defect-centered basis functions on these parameters were investigated. While specific results in excellent agreement with EPR measurements were obtained and strongly support the proposed defect model, inability to obtain overall agreement with experiment via a single c...

An ab initio study of the C 78 fullerene isomers

The five possible isolated-pentagon fullerene isomers of C 78 are investigated employing the Hartree—Fock self-consistent field method with minimal and double-zeta quality basis sets. Of the five structures, two have C 2v symmetry (C 2v(I) and C 2v(II)), two others have D 3h symmetry (D 3h(I) and D 3h(II)) and the last has D 3 symmetry. Experimentally, Diederich. reported the isolation of the C 2v(II) and D 3 isomers of C 78 formed in a ratio of ≈5:1. Kikuchi. later reported the isolation of C 78 in a mixture of C 2v(I), C 2v(II) and D 3 isomers formed in a ratio of 5:2:2, respectively. Previous theoretical studies employing qualitative methods have predicted the D 3h(II) isomer as the lowest energy structure, but this isomer has not been observed experimentally. Clearly, there is no agreement between the two experiments and previous theoretical studies of C 78. In this work, the predicted order of stability for the five isolated-pentagon isomers is found to be C 2v(I) > C 2v(II) > D 3 > D 3h(I) > D 3h(II) seems to correlate better with Kikuchi's experimental results.