Correlation Consistent Basis Sets Research Articles

Benchmarking Correlation-Consistent Basis Sets for Frequency-Dependent Polarizabilities with Multiresolution Analysis.

This paper presents the first converged frequency-dependent HF polarizability results for general molecules, on a set of 89 closed-shell atoms and molecules. The solver employs multiresolution analysis (MRA) in a multiwavelet basis to compute both ground and response states to a guaranteed precision, which are validated against independent numerical grid calculations on atoms and linear molecules. The MRA ground-state energies and response properties are used to evaluate results in correlation-consistent basis sets up to 5Z augmented with either single or double diffuse functions and core-polarization functions. Systematic trends are revealed through consideration of chemical composition as well as the use of machine learning to cluster convergence trends, the latter suggesting the possibility of learning and correcting basis-set error.

Probing Antioxidant-Related Properties for Phenolic Compounds.

In this work, properties related to antioxidant-potential mechanisms (such as the bond dissociation enthalpy, BDE, for the homolytic cleavage of the O-H bond and ionization energies, IEs) were determined for phenol, pyrocatechol, and gallic acid (GA). Both the protonated and deprotonated forms of GA were investigated. The Feller-Peterson-Dixon (FPD) composite method was employed with a variety of computational approaches, i.e., density functional theory, Möller-Plesset perturbation theory, and coupled-cluster-based methods, in combination with large correlation consistent basis sets with extrapolation to the complete basis set limit and consideration of core electron correlation effects. FPD results were compared to experimental and computational data available in the literature, presenting good agreement. For example, the FPD BDE (298 K) obtained for phenol, which was based on valence-correlated MP2/CBS calculations with contributions from correlating all electrons, was determined to be 87.56 kcal/mol, a value that is 0.42 kcal/mol lower than the result obtained in the most recent experiments, 87.98 ± 0.62. Calibration against coupled-cluster calculations was also carried out for phenol. We expect that the outcomes gathered here may help in establishing a general protocol for computational chemists that are interested in determining antioxidant-related properties for phenolic compounds with considerable accuracy as well as to motivate future IE measurements (particularly for GA) to be accomplished in the near future.

Theoretical Investigation on Electronic Excited States of the HSO Radical.

HSO radicals play an important role in the photochemical processes in combustion, the atmosphere, and the interstellar medium. In this work, we perform a high-level ab initio study on the electronic excited states of HSO using the internally contracted multireference configuration interaction methods including Davidson correction (icMRCI + Q) in combination with the correlation-consistent basis sets. The molecular geometries, vertical transition energies, oscillator strengths, and electronic configurations of 19 electronic states of HSO are computed. The electronic potential energy curves of HSO along the bond lengths and bond angles are presented. Based on our calculations, the interactions between the electronic states involved in the ultraviolet region and the mechanism of photodissociation are discussed, which will lay a foundation for revealing the dissociation dynamics of gas-phase HSO molecules in outer space and the earth's atmosphere.

New Schiff's base derivative and their nano‐sized Cr (III), Fe (III), Ru (III), and Ir (III) complexes: Preparation, DFT, characterization, bio‐catalytic, DNA interactions, cytotoxicity, and docking studies

Nano‐sized trivalent metal complexes of Cr (III), Fe (III), Ru (III), and Ir (III) were synthesized and characterized of the form [M (FMAVIEP)Cl2] where FMAVIEP = ligand (C14H11N2O2) and M = Cr (III), Fe (III), Ru (III), and Ir (III). Several spectral techniques studies were used to assess our trivalent metal complexes. The trivalent metal complexes' XRD results revealed sharp and intense diffraction peaks, signifying their crystalline properties at nanoscale particle size. Further evidence was obtained from images captured through techniques such as SEM, TEM, energy‐dispersive X‐ray, and AFM. These images confirmed the homogeneous distribution of the trivalent metal complexes over the surface of the complex. DFT studies were used to study the nano‐sized metal (III) complexes via the DFT\B3LYP computational approach, employing a 6–311G* correlation consistent basis set. The energy gap of synthesized complexes was inspected. The obtained data exhibited a strong correlation with the experimental ones, implying the bio‐efficiency of the Ru (III) complex. The absorption measurements for the nano‐sized complexes' interaction with CT‐DNA signify that nano‐sized metal (III) complexes bind through an intercalation mechanism. This conclusion is supported by the observed intrinsic binding constant (Kb) 3.33 × 105–5.84 × 105 M−1.

Ab Initio Conformational Analysis of 3,7-Diacetyl-3,7-Diazabicyclo[3.3.1]Nonanes

Introduction: The importance of the conformational behavior comprehension for proper prediction of properties for a certain compound or for a class of compounds is indisputable. For 3,7-diacylbispidines (3,7-diacyl-3,7-diazabicyclo[3.3.1]nonanes), only “double chair” (CC) conformers were prior found experimentally in the condensed phase, which differ only in the acyl groups relative orientation, “parallel,” pa or “antiparallel,” ap. However, 2 other conformer families, “boat-chair,” BC and “double twist,” TT, are known for other bicyclo[3.3.1]nonane derivatives. Features of these conformers would be useful for the accurate prediction of properties and activities of the compounds. Methods: Second-order perturbation theory ab initio techniques (MP2) in the triple-zeta correlation-consistent orbital basis set cc-pVTZ was employed to optimize the electronic energy for structures, to characterize the optimized structures as potential energy surface minima by energy hessian eigenvalue calculations and to calculate zero-point energy corrections for the minima using the “rigid rotor-harmonic oscillator” approximation to model the molecular ensemble thermodynamics. Additionally, the computational chemical thermodynamics benefits much from the concept of the molecular strain and its energy assessed successfully through the bond separation energy formalism. We combine both approaches in our investigation to find and consistently characterize the conformers previously unknown for the compounds under the studies. Results: Six possible conformers were found for the investigated 3,7-diacetyl-3,7-diazabicyclo[3.3.1]nonanes 1-4, formed by combining the skeletal conformation changes with the internal rotation of acyl substituents. The conformational behavior is quite similar for all investigated molecules. In all cases, the CC conformation is optimal for the bicyclic skeleton and ap orientation prevails over pa for 2 acetyl groups. This prevalence is 4-5 kcal mol−1 in CC and less than 1 kcal mol−1 in other skeletal forms, making rotation of 2 acyl groups in BC and TT almost independent. Concerning the skeletal conformations, the common energy sequence CC < BC < TT is found. While the relative BC energy is 6-7 kcal mol−1 over the optimal CC structure, TT forms are all strained by more than 12 kcal mol−1. Conclusions: For the first time, both BC and TT conformers of 3,7-diacetylbispidines were characterized by their strain and conformation energies together with known less strained CC forms. On the basis of our calculations, the relative energies of BC conformers are expected to be close to those of the CC acetyl amide bond rotamers found previously in experiment, therefore, their exclusion from the conformational behavior would look unjustified. On the contrary, TT conformers are found to be much more strained enough to be neglected in the conformational ensemble modeling.

Collisional excitation of propyne (CH3CCH) by He atoms

Context. A detailed interpretation of the detected emission lines of environments where propyne (or methyl acetylene, CH3CCH) is observed requires access to its collisional rate coefficients with the most abundant species in the interstellar medium, namely, helium (He) or molecular hydrogen (H2). Aims. We present the first three-dimensional potential energy surface (3D PES) for the CH3CCH-He molecular complex. We study the dynamics of the collision and report the first set of rate coefficients for temperatures up to 100 K for the collisional excitation of the lowest 60 ortho rotational levels and 60 para rotational levels of CH3CCH by He atoms. Methods. We computed the 3D PES with the explicitly correlated coupled-cluster with a single-, double-, and perturbative triple-excitation method in conjunction with the augmented correlation-consistent triple zeta basis set (CCSD(T)-F12a/aug-cc-pVTZ). The 3D PES was then fitted to an analytical function and scattering computations of pure rotational (de-)excitation of CH3CCH by collision with He atoms were performed. State-to-state cross-sections were computed using the close coupling method for total energies up to 100 cm−1 and with the coupled states approximation at higher energies for both the ortho- and para- symmetries of CH3CCH. Results. The PES we obtained is characterised by a large anisotropy and a potential well depth of 51.04 cm−1. By thermally averaging the collisional cross-sections, we determined the quenching rate coefficients for kinetic temperatures up to 100 K. A strong and even Δj propensity rule at almost all collision energies is present for CH3CCH-He complex. To evaluate the impact of rate coefficients on the analysis of observations, we carried out non-local thermodynamic equilibrium radiative transfer computations of the excitation temperatures and we demonstrate that local thermodynamic equilibrium conditions are not typically fulfilled for the propyne molecule.

Correlation consistent basis sets designed for density functional theory: Third-row atoms (Ga-Br).

The correlation consistent basis sets (cc-pVnZ with n = D, T, Q, 5) for the Ga-Br elements have been redesigned, tuning the sets for use for density functional approximations. Steps to redesign these basis sets for an improved correlation energy recovery and efficiency include truncation of higher angular momentum functions, recontraction of basis set coefficients, and reoptimization of basis set exponents. These redesigned basis sets are compared with conventional cc-pVnZ basis sets and other basis sets, which are, in principle, designed to achieve systematic improvement with respect to increasing basis set size. The convergence of atomic energies, bond lengths, bond dissociation energies, and enthalpies of formation to the Kohn-Sham limit is improved relative to other basis sets where convergence to the Kohn-Sham limit is typically not observed.

Developing correlation-consistent numeric atom-centered orbital basis sets for krypton: Applications in RPA-based correlated calculations.

Localized atomic orbitals are the preferred basis set choice for large-scale explicit correlated calculations, and high-quality hierarchical correlation-consistent basis sets are a prerequisite for correlated methods to deliver numerically reliable results. At present, numeric atom-centered orbital (NAO) basis sets with valence correlation consistency (VCC), designated as NAO-VCC-nZ, are only available for light elements from hydrogen (H) to argon (Ar) [Zhang et al., New J. Phys. 15, 123033 (2013)]. In this work, we extend this series by developing NAO-VCC-nZ basis sets for krypton (Kr), a prototypical element in the fourth row of the periodic table. We demonstrate that NAO-VCC-nZ basis sets facilitate the convergence of electronic total-energy calculations using the Random Phase Approximation (RPA), which can be used together with a two-point extrapolation scheme to approach the complete basis set limit. Notably, the Basis Set Superposition Error (BSSE) associated with the newly generated NAO basis sets is minimal, making them suitable for applications where BSSE correction is either cumbersome or impractical to do. After confirming the reliability of NAO basis sets for Kr, we proceed to calculate the Helmholtz free energy for Kr crystal at the theoretical level of RPA plus renormalized single excitation correction. From this, we derive the pressure-volume (P-V) diagram, which shows excellent agreement with the latest experimental data. Our work demonstrates the capability of correlation-consistent NAO basis sets for heavy elements, paving the way toward numerically reliable correlated calculations for bulk materials.

Systematic analysis of electronic barrier heights and widths for concerted proton transfer in cyclic hydrogen bonded clusters: (HF)n, (HCl)n and (H2O)n where n = 3, 4, 5.

The MP2 and CCSD(T) methods are paired with correlation consistent basis sets as large as aug-cc-pVQZ to optimize the structures of the cyclic minima for (HF)n, (HCl)n and (H2O)n where n = 3-5, as well as the corresponding transition states (TSs) for concerted proton transfer (CPT). MP2 and CCSD(T) harmonic vibrational frequencies confirm the nature of each minimum and TS. Both conventional and explicitly correlated CCSD(T) computations are employed to assess the electronic dissociation energies and barrier heights for CPT near the complete basis (CBS) limit for all 9 clusters. Results for (HF)n are consistent with prior studies identifying Cnh and Dnh point group symmetry for the minima and TSs, respectively. Our computations also confirm that CPT proceeds through Cs TS structures for the C1 minima of (H2O)3 and (H2O)5, whereas the process goes through a TS with D2d symmetry for the S4 global minimum of (H2O)4. This work corroborates earlier findings that the minima for (HCl)3, (HCl)4 and (HCl)5 have C3h, S4 and C1 point group symmetry, respectively, and that the Cnh structures are not minima for n = 4 and 5. Moreover, our computations show the TSs for CPT in (HCl)3, (HCl)4 and (HCl)5 have D3h, D2d, and C2 point group symmetry, respectively. At the CCSD(T) CBS limit, (HF)4 and (HF)5 have the smallest electronic barrier heights for CPT (≈15 kcal mol-1 for both), followed by the HF trimer (≈21 kcal mol-1). The barriers are appreciably higher for the other clusters (around 27 kcal mol-1 for (H2O)4 and (HCl)3; roughly 30 kcal mol-1 for (H2O)3, (H2O)5 and (HCl)4; up to 38 kcal mol-1 for (HCl)5). At the CBS limit, MP2 significantly underestimates the CCSD(T) barrier heights (e.g., by ca. 2, 4 and 7 kcal mol-1 for the pentamers of HF, H2O and HCl, respectively), whereas CCSD overestimates these barriers by roughly the same magnitude. Scaling the barrier heights and dissociation energies by the number of fragments in the cluster reveals strong linear relationships between the two quantities and with the magnitudes of the imaginary vibrational frequency for the TSs.

Insight into the Binding of Argon to Cyclic Water Clusters from Symmetry-Adapted Perturbation Theory.

This work systematically examines the interactions between a single argon atom and the edges and faces of cyclic H2O clusters containing three-five water molecules (Ar(H2O)n=3-5). Full geometry optimizations and subsequent harmonic vibrational frequency computations were performed using MP2 with a triple-ζ correlation consistent basis set augmented with diffuse functions on the heavy atoms (cc-pVTZ for H and aug-cc-pVTZ for O and Ar; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the two-body-many-body (2b:Mb) and three-body-many-body (3b:Mb) techniques; here, high-level CCSD(T) computations capture up through the two-body or three-body contributions from the many-body expansion, respectively, while less demanding MP2 computations recover all higher-order contributions. Five unique stationary points have been identified in which Ar binds to the cyclic water trimer, along with four for (H2O)4 and three for (H2O)5. To the best of our knowledge, eleven of these twelve structures have been characterized here for the first time. Ar consistently binds more strongly to the faces than the edges of the cyclic (H2O)n clusters, by as much as a factor of two. The 3b:Mb electronic energies computed with the haTZ basis set indicate that Ar binds to the faces of the water clusters by at least 3 kJ mol-1 and by nearly 6 kJ mol-1 for one Ar(H2O)5 complex. An analysis of the interaction energies for the different binding motifs based on symmetry-adapted perturbation theory (SAPT) indicates that dispersion interactions are primarily responsible for the observed trends. The binding of a single Ar atom to a face of these cyclic water clusters can induce perturbations to the harmonic vibrational frequencies on the order of 5 cm-1 for some hydrogen-bonded OH stretching frequencies.

Formation Mechanism of the Unsubstituted Chlorophosphazene Cl3P═NH: A Theoretical Study via Quantum Mechanical Calculations.

Although the synthesis of chlorophosphazene polymers has been explored for more than 100 years, the shortest yet most illusive monomer, Cl3P═NH, has never been isolated and fully characterized. Here we investigate the formation of Cl3P═NH from PCl5 and NH3 in chlorobenzene through quantum mechanical calculations. The potential energy surface was mapped using the MP2 Hamiltonian in conjunction with Dunning's correlation-consistent basis sets (aug-cc-pVXZ, where X = D and T). Along with HOMO/LUMO frontier molecular orbitals and natural bond orbital analyses, we found that instead of following the SN1 path proposed in the literature, the reaction proceeds via an addition-elimination mechanism. Our results also indicate that due to the low-lying stable intermediates (IM), most steps are exothermic such that the production of Cl3P═NH·2HCl can be completed once the energy barrier for the formation of [PCl4-NH3]+Cl- is overcome. Therefore, our theoretical work might explain the challenges in isolating any of the IMs in a typical chlorophosphazene reaction in chlorobenzene.

Use of Gaussian-Type Functions for Describing Fast Ion-Matter Irradiation with Time-Dependent Density Functional Theory.

The electronic stopping power is an observable property that quantifies the ability of swift ions to penetrate matter to transfer energy to the electron cloud. The recent literature has proven the value of Real-Time Time-Dependent Density Functional Theory to accurately evaluate this property from first-principles, but questions remain regarding the capability of computer codes relying on atom-centered basis functions to capture the physics at play. In this Perspective, we draw attention to the fact that irradiation by swift ions triggers electron emission into the continuum, especially at the Bragg peak. We investigate the ability of Gaussian atomic orbitals (AOC), which were fitted to mimic continuum wave functions, to improve electronic stopping power predictions. AOC are added to standard correlation-consistent basis sets or STO minimal basis sets. Our benchmarks for water irradiation by fast protons clearly advocate for the use of AOC, especially near the Bragg peak. We show that AOC only need to be placed on the molecules struck by the ion. The number of AOC that are added to the usual basis set is relatively small compared to the total number of atomic orbitals, making the use of such a basis set an excellent choice from a computational cost point of view. The optimum basis set combination is applied for the calculation of the stopping power of a proton in water with encouraging agreement with experimental data.

Formation of hydroxide anions in amorphous astrophysical ices and recombination with protons: a quantum chemical study

ABSTRACT Quantum chemical cluster calculations employing density functional theory and correlation consistent basis sets reveal the following pathways by which hydroxide anions (OH–) may form in amorphous astrophysical ices: (1) hydroxyl radicals (OH), which may arise in ice via ultraviolet photolysis, can capture electrons; (2) adsorbed hydrogen atoms can capture electrons to form H–, which reacts with water to yield H2 and OH–; (3) NaOH deposited on ice dissociates into Na+ and OH–; (4) NaH deposited on ice dissociates into Na+ and H–; H– then reacts with water to yield H2 and OH– as above. The IR spectrum of ice-bound OH– is presented, based on nine clusters containing up to 31H2O and 1–2 OH– anions. The interaction of OH– in ice with cations is also explored. Prior work shows that when HCO+ is deposited on pure amorphous water clusters, it reacts with H2O to form formic acid (HCOOH) and the hydronium (H3O+). When HCO+ is deposited on a cluster containing OH–, the reaction proceeds in almost the same manner, but the H3O+ and OH– charge centres migrate through the water network toward each other and tend to neutralize one another by forming H2O. This occurred in all but one of seven cases considered; migration occurred even when the oxygen atom attacked by HCO+ is over 10 Å from the oxygen atom in OH–. Cations and anions can interact in ice via pathways not present in the gas phase or incorporated in current models.

Competition between Solvent···Solvent and Solvent···Solute Interactions in the Microhydration of the Tetrafluoroborate Anion, BF4-(H2O)n=1,2,3,4.

This study systematically examines the interactions of the tetrafluoroborate anion (BF4-) with up to four water molecules (BF4-(H2O)n=1,2,3,4). Full geometry optimizations and subsequent harmonic vibrational frequency computations are performed using a variety of density functional theory (DFT) methods (B3LYP, B3LYP-D3BJ, and M06-2X) and the MP2 ab initio method with a triple-ζ correlation consistent basis set augmented with diffuse functions on all non-hydrogen atoms (cc-pVTZ for H and aug-cc-pVTZ for B, O, and F; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the CCSD(T) ab initio method and the haTZ basis set for the mono- and dihydrate (n = 1, 2) structures. The 2-body:Many-body (2b:Mb) technique, in which CCSD(T) computations capture the 1- and 2-body contributions to the interactions and MP2 computations recover all higher-order contributions, was used to extend these demanding computations to the tri- and tetrahydrate (n = 3, 4) systems. Four, five, and eight new stationary points have been identified for the di-, tri-, and tetrahydrate systems, respectively. The global minimum of the monohydrate adopts a symmetric double ionic hydrogen bond motif with C2v symmetry and an electronic dissociation energy of 13.17 kcal mol-1 at the CCSD(T)/haTZ level of theory. This strong solvent···solute interaction, however, competes with solute···solute interactions in the lowest-energy BF4-(H2O)n=2,3,4 minima that are not seen in the other di-, tri-, or tetrahydrate minima. The latter interactions help increase the 2b:Mb dissociation energies to more than 26, 41, and 51 kcal mol-1 for n = 2, 3, and 4, respectively. Structures that form hydrogen bonds between the solvating water molecules also exhibit the largest shifts in the harmonic OH stretching frequencies for the waters of hydration. These shifts can exceed -280 cm-1 relative to an isolated H2O molecule at the 2b:Mb/haTZ level of theory.

Accurate ab initio potential energy surface, rovibrational energy levels and resonance interactions of triplet ( 3 B1 ) methylene.

In this work, we report rovibrational energy levels for four isotopologues of methylene (CH2 , CHD, CD2 , and 13 CH2 ) in their ground triplet electronic state ( 3 B1 ) from variational calculation up to ~10,000 cm-1 and using a new accurate ab initio potential energy surface (PES). Triplet methylene exhibits a large-amplitude bending vibration and can reach a quasilinear configuration due to its low barrier (~2000 cm-1 ). To construct the ab initio PES, the Dunning's augmented correlation-consistent core-valence orbital basis sets were employed up to the sextuple-ζ quality [aug-cc-pCVXZ, X = T, Q, 5, and 6] combined with the single- and double-excitation unrestricted coupled cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. We have shown that the accuracy of the ab initio energies is further improved by including the corrections due to the scalar relativistic effects, DBOC and high-order electronic correlations. For the first time, all the available experimental rovibrational transitions were reproduced with errors less than 0.12 cm-1 , without any empirical corrections. Unlike more "traditional" nonlinear triatomic molecules, we have shown that even the energies of the ground vibrational state (000) with rather small rotational quantum numbers are strongly affected by the very pronounced rovibrational resonance interactions. Accordingly, the polyad structure of the vibrational levels of CH2 and CD2 was analyzed and discussed. The comparison between the energy levels obtained from the effective Watson A-reduced Hamiltonian, from the generating-function approach and from a variational calculation was given.

Benchmarking Time-dependent Density Functional Theory for the prediction of electronic absorption spectra of amorphous ices for astrochemical applications

ABSTRACT Time-dependent density functional theory (TDDFT) offers a tractable means to predict electronic excitation spectra of ices if sufficient care is taken in selecting the DFT functional, basis sets, and the number of excited states. In this work 48 functionals in conjunction with various correlation consistent basis sets were benchmarked for predicting electronic spectra. A training set of important astromolecules was chosen: carbon monoxide, water, hydrogen cyanide, ammonia, methanol, and the hydroxyl radical. Vertical excitation energies between the ground and first excited state and some higher excited states were calculated using multireference configuration interaction calculations to serve as benchmarks for gas phase TDDFT calculations. When used in conjunction with aug-cc-pVDZ quality correlation consistent basis sets, two functionals, MPW1K and ωB97, emerged as very good choices to model electronic excitations for most of the molecules in the training set. Cluster calculation predictions for the UV spectra of amorphous ices of water and ammonia were performed at the TDDFT-MPW1K/AVDZ and TDDFT-ωB97/AVDZ levels and then compared against experimental data. The calculations qualitatively reproduce the shapes of the spectra for the most part and quantitatively predict the position of the critical first absorption peak.

Theoretical Study on the Spectroscopic Properties and Photodissociation Mechanism of Dibromocarbene.

Detailed calculations on the electronic states of dibromocarbene (CBr2) herein are presented. First, the spectroscopic properties of the electronic states including geometry parameters, harmonic vibrational frequencies and transition energies of the lowest electronic states of the neutral radical were calculated in detail using the internally contracted multireference configuration interaction methods including Davidson correction (icMRCI+Q) with correlation consistent basis sets of aug-cc-pVXZ (X = T, Q, 5). Second, as CBr2 including two Br atoms, the Spin-Orbit Coupling (SOC) effect on the spectroscopic parameters and the one-dimensional cuts of the potential energy surface (PESs) of the lowest three states were studied. The barrier to linearity and dissociation of the singlet state were discussed. Third, the one-dimensional cuts along with the vertical transition energy (VTE), the oscillator strength, and so on of the electronic states related to the several lowest dissociation limits of CBr2 were calculated at the icMRCI+Q/aug-cc-pVTZ level. Based on the computed results of the electronic states of the radical, the photodissociation mechanism in the UV region were discussed in detail. The ab initio calculations are compared with the previous theoretical and experimental data and are in good agreement. The present work will provide a comprehensive understanding on the electronic structures and dissociation dynamics for the electronic states of the CBr2 radical.

Basis Set Effects on the Stabilities and Interaction Energies of Small Amide Molecules Adsorbed on Kaolinite Surface

Adsorptions of small amide molecules, acetamide (AA) and N-methyl-acetamide (NMA) on the surface of kaolinite are investigated in this study. The focus is on the basis set effects towards the stabilities and the interaction energies of the molecules on the Al–O surface. With a fixed B3LYP functional, we increased the size of the basis sets for the single-point calculations, to find the converged interaction energies and obtain the relative stabilities. We found that, under the direct usage of Pople-type and Dunning’s correlation consistent basis sets, it is not possible to achieve the pattern of convergence for the interaction energies and the relative stabilities. Compared to the complete basis set (CBS) extrapolation scheme, the double zeta basis sets deviated the most, in the range of 21 to 27%, while it is from 1 to 7% for the triple zeta basis sets. Based on the results, we suggest using 6-311++G(2df,2pd) or cc-pVQZ for energy-related quantities. Compared to AA, NMA attached more strongly by 0.5 eV on the surface of Al–O.

Correlation Consistent Basis Sets for Explicitly Correlated Theory: The Transition Metals.

We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f2g] for the 3d-block elements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters.

Reproducibility of calculations on Li species with correlation-consistent basis sets

We have found that two different basis set series, both labeled cc-pVxZ, are widely available and widely used for calculation on Li compounds such that calculations that should be the same are different, causing a reproducibility problem. Here we study the magnitude of the disagreement of these nominally-the-same basis sets for wave function and density functional calculations of Li clusters. We find deviations among the basis sets of as large as 22 millihartrees. In most cases one obtains lower energies with the noncanonical choices. Therefore, it is important to specify which version of the basis set is used for calculations.