Quadruple-ζ Quality Basis Sets Research Articles

Ni, Cu, Zn, Pd, Ag and Cd Tetraphenylporphyrin Ab Initio Thermochemistry: Enthalpy of Formation of ZnTPP Revisited.

Groups 10-12 metalloporphyrins have been recognized for their numerous properties essential for the development of new sensing materials. In this work, accurate gas-phase enthalpies of formation, ΔfHm0(g,298.15), are predicted for the series of Ni, Cu, Zn, Pd, Ag, and Cd tetraphenylporphyrins (MTPPs) on the basis of the reaction-based Feller-Peterson-Dixon approach and high-level ab initio DLPNO-CCSD(T) calculations. Our recently developed automatic generator of the balanced chemical reactions was employed to reduce the bias of the theoretical ΔfHm0(g,298.15) toward a particular reaction. Theoretical ΔfHm0(g,298.15) for ZnTPP (227.0 ± 3.4 kcal mol-1) does not support the previously reported experimental value of 132 ± 2 kcal mol-1. The origin of the discrepancy probably lies in the experimental solid-state ΔfHm0(ZnTPP, cr,298.15) as it stems from our theoretical evaluations of the ΔfHm0(cr,298.15) values for the entire set of transition metal TPP complexes. The large discrepancy between experiment and theory also holds when different DFT functionals (ωB97M-V, PBE0-D4, and B3LYP-D4) paired with quadruple-ζ quality basis sets are used for the theoretical calculations. Experimental revisiting of the solid-state enthalpy of formation of ZnTPP and analogue measurements for other transition metal TPPs are needed to resolve the observed discrepancy. Based on the predicted enthalpies of formation of MTPPs, the relative energies of the metal-ligand bonding are evaluated and the trends are compared to those for the complexes of the unsubstituted porphyrin with the same set of metals derived in [Can. J. Chem., 2009, 87, 1063]. According to both studies, Pd complexes exhibit the strongest bonding, while the Cd species are the least stable metallocomplexes within the considered series.

New pecJ-n (n = 1, 2) Basis Sets for High-Quality Calculations of Indirect Nuclear Spin-Spin Coupling Constants Involving 31P and 29Si: The Advanced PEC Method.

In this paper, we presented new J-oriented basis sets, pecJ-n (n = 1, 2), for phosphorus and silicon, purposed for the high-quality correlated calculations of the NMR spin–spin coupling constants involving these nuclei. The pecJ-n basis sets were generated using the modified version of the property-energy consistent (PEC) method, which was introduced in our earlier paper. The modifications applied to the original PEC procedure increased the overall accuracy and robustness of the generated basis sets in relation to the diversity of electronic systems. Our new basis sets were successfully tested on a great number of spin–spin coupling constants, involving phosphorus or/and silicon, calculated within the SOPPA(CCSD) method. In general, it was found that our new pecJ-1 and pecJ-2 basis sets are very efficient, providing the overall accuracy that can be characterized by MAEs of about 3.80 and 1.98 Hz, respectively, against the benchmark data obtained with a large dyall.aae4z+ basis set of quadruple-ζ quality.

Segmented Contracted Error-Consistent Basis Sets of Quadruple-ζ Valence Quality for One- and Two-Component Relativistic All-Electron Calculations.

Segmented contracted basis sets of quadruple-ζ quality for exact two-component (X2C) calculations are presented for the elements H-Rn. These sets are the all-electron relativistic counterparts of the Karlsruhe "def2" and "dhf" systems of bases, which were designed for Hartree-Fock and density functional treatments and-with a somewhat extended set-also for correlated treatments. The bases were optimized with analytical basis set gradients and the finite nucleus model based on a Gaussian charge distribution at the scalar-relativistic X2C level. Extensions are provided for self-consistent two-component treatments to describe spin-orbit coupling, polarization effects, and nuclear magnetic resonance (NMR) shielding constants. The basis sets were designed to yield comparable errors in atomization energies, orbital energies, dipole moments, and NMR shielding constants all across the periodic table of elements. A test set of more than 360 molecules representing (nearly) all elements in their common oxidation states was utilized for the valence properties, and a test set of more than 250 closed-shell molecules was employed for the NMR shielding constants. The quality of the developed basis sets is compared to other frequently used relativistic all-electron bases.

Determination of accurate semiexperimental equilibrium structure of proline using efficient transformations of anharmonic force fields among the series of isotopologues

ABSTRACTThe complete semiexperimental (SE) equilibrium structure of proline (45 degrees of freedom) is determined using the mixed estimation method. The cubic force fields for the parent and eight isotopologues of proline molecule are evaluated at the MP2-FC/cc-pVTZ level in Cartesian coordinates. The accuracy of the SE structure is verified by optimising the structure with the CCSD(T) model and a basis set of quadruple-ζ quality. A significantly more accurate equilibrium structure of proline is obtained when compared to the previous one. It is shown that the employed technique is efficient for the determination of SE equilibrium structures of rather large molecules. A simple transformation of anharmonic force fields between normal coordinate and Cartesian coordinate representations is proposed. The suggested technique allows efficient evaluation of the rotation–vibration interaction constants for a number of isotopologues, once the cubic force field of any species is found either in normal or Cartesian coordinates.

Relativistic Prolapse-Free Gaussian Basis Sets of Quadruple-ζ Quality: (aug-)RPF-4Z. III. The f-Block Elements

The f-block elements are addressed in this third part of a series of prolapse-free basis sets of quadruple-ζ quality (RPF-4Z). Relativistic adapted Gaussian basis sets (RAGBSs) are used as primitive sets of functions while correlating/polarization (C/P) functions are chosen by analyzing energy lowerings upon basis set increments in Dirac-Coulomb multireference configuration interaction calculations with single and double excitations of the valence spinors. These function exponents are obtained by applying the RAGBS parameters in a polynomial expression. Moreover, through the choice of C/P characteristic exponents from functions of lower angular momentum spaces, a reduction in the computational demand is attained in relativistic calculations based on the kinetic balance condition. The present study thus complements the RPF-4Z sets for the whole periodic table (Z ≤ 118). The sets are available as Supporting Information and can also be found at http://basis-sets.iqsc.usp.br .

Accurate Determination of Equilibrium Structure of 3-Aminophthalonitrile by Gas Electron Diffraction and Coupled-Cluster Computations: Structural Effects Due to Intramolecular Charge Transfer.

For the first time, the molecular structure of 3-aminophthalonitrile with unique electronic properties has been determined by the gas electron diffraction (GED) method supported by a mass spectrometric analysis of the gas phase. Moreover, it has been optimized at the high-level quantum-chemical coupled-cluster theory, CCSD(T), in conjunction with the triple-ζ basis set. The equilibrium structure has been determined from the GED data taking into account harmonic and anharmonic vibrational corrections estimated from the quantum-chemical force field (up to cubic terms). The computed CCSD(T) structure has been corrected for the core-core and core-valence electron-correlation effects estimated at the MP2 level and extrapolated to the basis set of quadruple-ζ quality. A remarkable agreement between the experimental and theoretical equilibrium structural parameters (bond lengths and angles) points to a high accuracy of both the molecular structure and applied theories. The high accuracy of structure computations and experimental determination allows the observation of structural changes due to the intramolecular charge transfer predicted by natural bond orbital (NBO) calculations. According to the NBO analysis, the amino group is the electron-donating substituent, whereas the nitrile groups are able to withdraw the π electrons from the benzene ring. Noticeable variations in the structural parameters are also explained by the interaction of σ → π* orbitals of the nearest C≡N and N-H bonds.

A Static Picture of the Relaxation and Intersystem Crossing Mechanisms of Photoexcited 2-Thiouracil.

Accurate excited-state quantum chemical calculations on 2-thiouracil, employing large active spaces and up to quadruple-ζ quality basis sets in multistate complete active space perturbation theory calculations, are reported. The results suggest that the main relaxation path for 2-thiouracil after photoexcitation should be S2 → S1 → T2 → T1, and that this relaxation occurs on a subpicosecond time scale. There are two deactivation pathways from the initially excited bright S2 state to S1, one of which is nearly barrierless and should promote ultrafast internal conversion. After relaxation to the S1 minimum, small singlet–triplet energy gaps and spin–orbit couplings of about 130 cm–1 are expected to facilitate intersystem crossing to T2, from where very fast internal conversion to T1 occurs. An important finding is that 2-thiouracil shows strong pyramidalization at the carbon atom of the thiocarbonyl group in several excited states.

Domain Based Pair Natural Orbital Coupled Cluster Studies on Linear and Folded Alkane Chains.

In this study the question of what is the last unbranched alkane that prefers a linear conformation over a folded one is revisited from a theoretical point of view. Geometries have been optimized carefully using the most accurate theoretical approach available to date for such systems, namely, doubly hybrid density functional theory in conjunction with larger quadruple-ζ quality basis sets. The resulting geometries deviate significantly from previously reported ones and have a significant impact on the predicted energetics. Electronic energies were calculated using the efficient and accurate domain local pair natural orbital coupled cluster method with single-, double-, and triple substitutions (DLPNO-CCSD(T)) electronic structure method. Owing to the method's efficiency, we were able to employ up to quadruple-ζ quality basis sets for all hydrocarbons up to C19H40. In conjunction with carefully designed basis set extrapolation techniques, it is estimated that the electronic energies reported in this study deviate less than 1 kJ/mol from the canonical CCSD(T) basis set limit. Thermodynamic corrections were calculated with the PW6B95-D3 functional and the def2-QZVP basis set. Our prediction is that the last linear conformer is either C16H34 or C17H36 with the latter being more probable. C18H38 can be safely ruled out as the most stable isomer at 100 K. These findings are in agreement with the elegant experimental studies of Suhm and co-workers. Deviations between the current and previous theoretical results are analyzed in detail.

HM⁺-RG complexes (M = group 2 metal; RG = rare gas): Physical vs. chemical interactions.

Previous work on the HM(+)-He complexes (M = Be-Ra) has been extended to the cases of the heavier rare gas atoms, HM(+)-RG (RG = Ne-Rn). Optimized geometries and harmonic vibrational frequencies have been calculated using MP2 theory and quadruple-ζ quality basis sets. Dissociation energies for the loss of the rare gas atom have been calculated at these optimized geometries using coupled cluster with single and double excitations and perturbative triples, CCSD(T)theory, extrapolating interaction energies to the basis set limit. Comparisons are made between the present data and the previously obtained helium results, as well as to those of the bare HM(+) molecules; furthermore, comparisons are made to the related M(+)-RG and M(2+)-RG complexes. Partial atomic charge analyses have also been undertaken, and these used to test a simple charge-induced dipole model. Molecular orbital diagrams are presented together with contour plots of the natural orbitals from the quadratic configuration with single and double excitations (QCISD) density. The conclusion is that the majority of these complexes are physically bound, with very little sharing of electron density; however, for M = Be, and to a lesser extent M = Mg, some evidence for chemical effects is seen in HM(+)-RG complexes involving RG atoms with the higher atomic numbers.

Theoretical Study of M(+)-RG2: (M(+) = Ca, Sr, Ba, and Ra; RG = He-Rn).

Ab initio calculations were employed to investigate M(+)-RG2 species, where M(+) = Ca, Sr, Ba, and Ra and RG = He-Rn. Geometries have been optimized, and cuts through the potential energy surfaces containing each global minimum have been calculated at the MP2 level of theory, employing triple-ζ quality basis sets. The interaction energies for these complexes were calculated employing the RCCSD(T) level of theory with quadruple-ζ quality basis sets. Trends in binding energies, De, equilibrium bond lengths, Re, and bond angles are discussed and rationalized by analyzing the electronic density. Mulliken, natural population, and atoms-in-molecules (AIM) population analyses are presented. It is found that some of these complexes involving the heavier group 2 metals are bent whereas others are linear, deviating from observations for the corresponding Be and Mg metal-containing complexes, which have all previously been found to be bent. The results are discussed in terms of orbital hybridization and the different types of interaction present in these species.

Relativistic Prolapse-Free Gaussian Basis Set of Quadruple-ζ Quality: (aug-)RPF-4Z. II. The d-Block Elements.

A series of relativistic prolapse-free Gaussian basis sets of quadruple-ζ quality has been developed: (aug-)RPF-4Z. Here, we report the (aug-)RPF-4Z sets for all the d-block elements (Sc-Cn). Molecular calculations at the Coupled Cluster level showed a significant reduction in computational demand in comparison with other well-known relativistic quadruple-ζ sets. The (aug-)RPF-4Z sets in a ready-to-use format are available as Supporting Information and can also be found at http://basis-sets.iqsc.usp.br/.

Prediction of Reaction Barriers and Thermochemical Properties with Explicitly Correlated Coupled-Cluster Methods: A Basis Set Assessment

We assessed the performance of our perturbative explicitly correlated coupled-cluster method, CCSD(T)F12, for accurate prediction of chemical reactivity. The reference data included reaction barrier heights, electronic reaction energies, atomization energies, and enthalpies of formation from the following sources: (1) the DBH24/08 database of 22 reaction barriers (Truhlar et al.), (2) the HJO12 set of isogyric reaction energies (Helgaker et al.), and (3) a HEAT set of atomization energies and heats of formation (Stanton et al.). We performed two types of analyses targeting the two distinct uses of explicitly correlated CCSD(T) models: as a replacement for basis-set-extrapolated CCSD(T) in highly accurate composite methods like HEAT and as a distinct model chemistry for standalone applications. Hence, we analyzed in detail (1) the basis set error of each component of the CCSD(T)F12 contribution to the chemical energy difference in question and (2) the total error of the CCSD(T)F12 model chemistry relative to the benchmark values. Two basis set families were utilized in the calculations: the standard aug-cc-p(C)VXZ-F12 (X = D, T, Q) basis sets for the conventional correlation methods and the cc-p(C)VXZ-F12 (X = D, T, Q) basis sets of Peterson and co-workers that are specifically designed for explicitly correlated methods. Our conclusion is that the performance of the two families for CCSD correlation contributions (which are the only components affected by the explicitly correlated terms in our formation) are nearly identical with triple- and quadruple-ζ quality basis sets, with some differences at the double-ζ level. Chemical accuracy (∼4.18 kJ/mol) for reaction barrier heights, electronic reaction energies, atomization energies, and enthalpies of formation is attained on average with the aug-cc-pVDZ, aug-cc-pVTZ, cc-pCVTZ-F12/aug-cc-pCVTZ, and cc-pCVDZ-F12 basis sets, respectively, at the CCSD(T)F12 level of theory. The corresponding mean unsigned errors are 1.72 kJ/mol, 1.5 kJ/mol, ∼2 kJ/mol, and 2.17 kJ/mol, and the corresponding maximum unsigned errors are 4.44 kJ/mol, 3.6 kJ/mol, ∼5 kJ/mol, and 5.75 kJ/mol.

Spectroscopy and dissociation of I2–Rg (Rg = Kr and Xe) van der Waals complexes

The spectroscopy and dissociation of I2–Rg (Rg = Kr and Xe) van der Waals complexes have been studied in detail using MP2 and CCSD(T) methods in conjunction with the correlation-consistent triple-ζ and quadruple-ζ quality basis sets. The large-core Stuttgart–Dresden–Bonn (SDB) relativistic pseudopotential is used for all heavy elements. The dissociation energy and depth of the potential well have been calculated using potential method and supermolecular approach in order to remove the discrepancy among the existing theoretical and experimental values. Most of the spectroscopic properties are first reported, and the rest agree very well with the theoretical and experimental values wherever available.

Accurate determination of an equilibrium structure in the presence of a small coordinate: The case of dimethylsulfide

The ab initio structure of dimethylsulfide is calculated at the CCSD(T) level of theory using a basis set of quadruple-ζ quality which takes into account the core correlation. The quadratic, cubic and semi-diagonal quartic force field of dimethylsulfide is calculated at the MP2 level of theory employing a basis set of triple-ζ quality. A semi-experimental equilibrium structure is derived from experimental ground-state rotational constants and rovibrational interaction parameters calculated from the ab initio force field. In spite of a very large number of isotopologues, the position of the in-plane hydrogens is poorly defined. This is explained by the small b-coordinate of these atoms. The problem is solved using the merged least-squares method where the input data are the semi-experimental and the ab initio structures.

The Smallest “Aurophilic Species”

The existence of the C2v symmetric closed-shell di[gold(I)]hydronium cation [Au2H]+ (1), is predicted. It is shown that 1 is the smallest possible molecular species containing aurophilic contacts. Equilibrium structural parameters, vibrational frequencies and formation energies of 1 from Au+ and AuH, have been calculated, employing a series of highly correlated but available standard relativistic ab initio methods up to CCSD(T) level of theory and all-electron basis sets of quadruple-ζ quality with double polarizations. Relativistic effects have been taken into account by employing pseudorelativistic electron core potentials (ECP) or a scalar relativistic treatment using a Douglas-Kroll-Heß Hamiltonian of 2nd, 3rd and 4th order (DKH2, DKH3, DKH4).

Torsional barrier and equilibrium structure of ethyl cyanide

The quadratic, cubic and semi-diagonal quartic force field of ethyl cyanide has been calculated at the B3LYP level of theory employing a basis set of triple-ζ quality. A semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational interaction parameters calculated from the ab initio force field. This structure is in excellent agreement with the ab initio structure calculated at the CCSD(T) level of theory using a basis set of quadruple-ζ quality and a core correlation correction. The empirical structures are also determined and their accuracy is discussed. The potential barrier V 3 hindering internal rotation of the methyl group has been calculated from 23 rotational transitions of CH 3CH 2C 15N which were found split into doublets, giving V 3 = 3074(27) cal mol −1.

Ab initio anharmonic force field and equilibrium structure of vinyl bromide

The quadratic, cubic, and semi-diagonal quartic force field of vinyl bromide has been calculated at the MP2 level of theory employing a basis set of triple-ζ quality including a relativistic pseudopotential on bromine. A semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational interaction parameters calculated from the ab initio force field. This structure is in excellent agreement with the ab initio structure calculated at the CCSD(T) level of theory using a basis set of quadruple-ζ quality and an offset correction. The experimental mass-dependent r m structures are also determined and their accuracy is discussed.

Basis Set Requirements for Sulfur Compounds in Density Functional Theory: a Comparison between Correlation-Consistent, Polarized-Consistent, and Pople-Type Basis Sets

We have investigated the SX (X = first- or second-row atom), SO2, and SO3 molecules employing the correlation-consistent (cc), the recently developed polarization-consistent (pc), and three Pople-type basis sets, in conjunction with the B3LYP functional. The results confirmed that the aug-pc basis sets represent a great contribution in terms of cost-benefits. In the case of the B3LYP functional, when employing the aug-pc-3 and aug-pc-4 basis sets, it is possible to obtain results that are of aug-cc-pV(5+d)Z and aug-cc-pV(6+d)Z quality, respectively, at a much lower cost. The estimations obtained employing smaller members of the family are of nearly double-ζ quality and do not provide reliable results. There is no basis set of quadruple-ζ quality among the polarized-consistent basis sets, although in terms of composition, the aug-pc-3 basis set is a QZ basis set. A precise estimation of the Kohn-Sham complete basis set (CBS) limit with the aug-pc-X basis sets is too difficult for the B3LYP functional because the ∞(aug-pc-4, aug-pc-3, aug-pc-2) extrapolation gives the same results as those of the aug-pc-4 basis set. This is in contrast with the results observed for ab initio methodologies for which the largest basis sets provided the best estimation of the CBS limit. In our opinion, the closest results to the B3LYP/CBS limit are expected to be those obtained with a two-point extrapolation employing the aug-cc-pV(X+d)Z (X = 5, 6) basis sets. The results obtained with this extrapolation are very close to those predicted by the ∞(aug-pc-3, aug-pc-2, aug-pc-1) extrapolation, and that provides a cheaper but more inaccurate alternative to estimate the CBS limit. Minor problems were found for the aug-pc-X basis sets and the B3LYP functional for molecules in which sulfur is bound to a very electronegative element, such as SO, SF, SO2, and SO3. For these molecules, the cc basis sets were demonstrated to be more useful. The importance of tight d functions was observed; the total atomization energy of SO2 employing the cc-pV6Z basis set is 1 kcal/mol lower than that obtained with the aug-cc-pV(6+d)Z basis set.

Coupled Cluster CCSD(T) Calculations of Equilibrium Geometries, Anharmonic Force Fields, and Thermodynamic Properties of the Formyl (HCO) and Isoformyl (COH) Radical Species

The HCO and COH formyl radical species were studied by the coupled cluster electron correlation technique and using the augmented correlation consistent polarized core-valence basis sets of quadruple-ζ quality. The complete basis set limits for the equilibrium geometry and spectroscopic parameters of HCO were estimated: Re(CH) = 1.117 A; Re(CO) = 1.174 A; αe(HCO) = 124.6°. The COH isomerization energy is equal to 176 kJ/mol. The energy of the COH → HCO transition state is equal to 107 kJ/mol. The heat of formation was found using the basis set of cc-pcv5z quality: ΔfH°(298.15) = 42.3 for HCO and 218.1 kJ/mol for COH. The thermochemistry of HCO and COH was studied beyond the rigid rotor harmonic oscillator approach. The results were compared with available experimental data and results of previous calculations.

Potential Energy Surface and Vibrational−Rotational Energy Levels of Hydrogen Peroxide

The six-dimensional potential energy surface of hydrogen peroxide, H2O2, has been determined from large-scale ab initio calculations using the coupled-cluster method, CCSD(T), with the basis set of quadruple-ζ quality, cc-pVQZ. The effects of core-electron correlation on the calculated structural parameters and the torsional potential energy function have been investigated. The anharmonic quartic force field has been determined. The vibrational−rotational energy levels of the molecule have then been calculated using the variational method. The calculated molecular properties are found to be in good agreement with experimental data.