Complete Basis Set CCSD Research Articles

Composite ab initio vibrational spectroscopy and thermochemistry of low-valency lanthanide compounds: europium dihalides EuX2 (X = F, Cl, Br, I).

A unique diversity in chemical properties of lanthanide compounds making them very useful in various important applications stems not least from the existence of less common Ln oxidation states, in particular +2. However, the molecular properties of low-valency lanthanide compounds are not yet well studied even for the most stable divalent Ln-containing species, such as europium dihalides. In this paper, highly accurate molecular structures, vibrational spectra, and atomisation energies of the europium dihalides EuX2 (X = F, Cl, Br, I) are obtained at the complete basis set CCSD(T) level. All of the EuX2 species are calculated to be non-linear (C2v) exhibiting a regular increase in X-Eu-X bond angle on passing through the halogen series (F → Cl → Br → I), from 117° in EuF2 to 141° in EuI2, which is accompanied by a rapid decrease in the barriers to linearity, h = E(D∞h) - E(C2v), from 2180 cm-1 to 166 cm-1, respectively. The Eu-X bonds in EuX2 appear to be longer but energetically stronger than those in the respective monohalides EuX, whose properties are studied in this work at the same level of theory as EuX2. The performance of the Ln 4f-in-core pseudopotential (PP) approximation for EuX2 is assessed by comparing the Eu PP-based coupled-cluster (CC) calculations with all-electron CC benchmarks. Incorporating the Eu 4f electrons into the PP is shown to cause large errors: up to 10 deg. in X-Eu-X bond angles, 80% in barriers to linearity, and 0.05 Å in the Eu-X bond lengths, which proves the necessity of an explicit treatment of 4f electrons if high accuracy is the goal. The present results set a benchmark in the field of low-valency lanthanide chemistry, in particular for the calibration of DFT functionals.

Simple Composite Approach to Efficiently Estimate Basis Set Limit CCSD(T) Harmonic Frequencies and Reaction Thermochemistry.

We introduce a simple strategy that combines the G3(MP2) composite method and explicitly correlated coupled cluster CCSD(T)-F12 method to efficiently estimate complete basis set CCSD(T) molecular geometries and harmonic vibrational frequencies at the cost of a double-ζ basis set calculation. Based on a large test set of 61 neutral, ionic, and open-shell molecules, and additionally 31 molecules in the HFREQ2014 data set, we demonstrate that this composite strategy has an average accuracy of 2 cm-1 or better relative to complete basis set CCSD(T) values. Using this approach, we estimated 696 CCSD(T)/CBS reaction energies of small to medium-sized systems containing up to 6 heavy atoms and confirmed existing approximations that use small basis set density functional theory methods [e.g., M06-2X/6-31+G(d)] to calculate thermal contributions to reaction enthalpies and Gibbs free energies that are accurate to within 0.2 kcal mol-1 on average.

Accurate spectroscopy, dipole moment, and ionization energy of gadolinium monoxide from high-level electronic structure calculations

A complete-basis-set (CBS) coupled-cluster composite approach including core correlation, spin–orbit coupling, and higher-order correlation up to CCSDT(Q) is used to determine the GdO and GdO+ bond dissociation energies (BDE) and GdO ionization energy (IE). Composite BDE(GdO+) and IE(GdO) are superior in accuracy to their experimental counterparts, differing from the latter by more than 0.3 eV. The CBS CCSD(T) spectroscopic constants re, ωe, ωexe, and αe of GdO and GdO+ and dipole moment of GdO are reported for the first time.

Electronic Energies Are Not Enough: An Ion Mobility-Aided, Quantum Chemical Benchmark Analysis of H+GPGG Conformers.

Peptides and proteins exist not as single, lowest energy structures but as ensembles of states separated by small barriers. In order to study these species we must be able to correctly identify their gas phase conformational distributions, and ion mobility spectrometry (IMS) has arisen as an experimental method for assessing the gas phase energetics of flexible peptides. Here, we present a thorough exploration and benchmarking of the low energy conformers of the small, hairpin peptide H+GPGG with the aid of ion mobility spectrometry against a wide swath of density functionals (35 dispersion-corrected and uncorrected functionals represented by 21 unique exchange-correlation functionals) and wave function theory methods (15 total levels of theory). The three experimentally resolved IMS peaks were found to correspond to three distinct pairs of conformers, each pair composed of species differing only by the chair or boat configuration of the proline. Two of the H+GPGG conformer pairs possess a cis configuration about the Pro-Gly1 peptide bond while the other adopts a trans configuration. While the experimental spectrum reports a higher intensity for the cis-1 conformer than the trans conformer, 13 WFT levels of theory, including a complete basis set CCSD(T) extrapolation, obtain trans to be favored in terms of the electronic energy. This same effect is seen in 14 of the 18 dispersion-corrected density functionals studied, whereas the remaining 17 functionals show more variety. Only when Gibbs free energies are considered do the WFT methods and dispersion-corrected functionals reflect the experimental distribution. CAM-B3LYP-D3BJ emerges as the best-performing density functional, matching the experimental distribution and the CCSD(T)/CBS relative energies within 6%. Further analysis reveals the trans conformer to be favored electronically, but entropically disfavored, leading to the experimental preference of the cis-1 conformer. These results highlight the danger in considering only the electronic energies, which is common practice in electronic structure theory predictions of conformational energy distributions. Additionally, the effects of temperature and scaling of the frequencies used in obtaining the Gibbs free energies are explored.

Exploring the Rich Potential Energy Surface of (H2O)11 and Its Physical Implications.

The rich potential energy surface of the water undecamer (H2O)11 was explored with a basin hopping algorithm using a TIP4P potential and other methods followed by extensive ab initio MP2 minimizations and CCSD(T) corrections. This protocol yielded 17, 66, and 125 distinct isomers within 0.5, 1.0, and 2.0 kcal mol-1 of the complete basis set CCSD(T) global minimum, respectively. These isomers were categorized into 15 different families based on their oxygen framework and hydrogen bonding topology. Determination of the global minimum proved challenging because of the presence of many nearly isoenergetic isomers. The predicted global minimum varied among ab initio methods, density functionals, and model potentials, and it was sensitive to the choice of energy extrapolation schemes, higher-order CCSD(T) corrections, and inclusion of zero-point vibrational energy. The presence of a large number of nearly degenerate structures and the isomerization between them has manifested itself in the anomalous broadening of the heat capacity curve of the undecamer in simulations around the melting region.

Comparative Study of Methanol Activation by Different Small Mixed Silicon Clusters Si2M with M = H, Li, Na, Cu, and Ag.

High-accuracy quantum chemical calculations were carried out to study the mechanisms and catalytic abilities of various mixed silicon species Si2M with M = H, Li, Na, Cu, and Ag toward the first step of methanol activation reaction. Standard heats of formation of these small triatomic Si clusters were determined. Potential-energy profiles were constructed using the coupled-cluster theory with extrapolation to complete basis set CCSD(T)/CBS, and CCSD(T)/aug-cc-pVTZ-PP for Si2Cu and Si2Ag. The most stable complexes generated by the interaction of methanol with the mixed clusters Si2M possess low-spin states and mainly stem from an M–O connection in preference to Si–O interaction, except for the Si2H case. In two competitive pathways including O–H and C–H bond breakings, the cleavage of the O–H bond in the presence of all clusters studied becomes predominant. Of the mixed clusters Si2M considered, the dissociation pathways of both O–H and C–H bonds with Si2Li turns out to have the lowest energy barriers. The most remarkable finding is the absence of the overall energy barrier for the O–H cleavage with the assistance of Si2Li. The breaking of O–H and C–H bonds with the assistance of Si2H, Si2Li, and Si2Na is kinetically preferred with respect to the Si2Cu and Si2Ag cases, apart from the case of Si2Na for O–H cleavage. In comparison with other transition-metal clusters with the same size, such as Cu3, Pt3, and PtAu2, the energy barriers for the O–H bond activation in the presence of small Si species, especially Si2H and Si2Li, are found to be lower. Consequently, these small mixed silicon clusters can be regarded as promising alternatives for the expensive metal-based catalysts currently used for methanol activation particularly and other dehydrogenation processes of organic compounds. The present study also suggests a further extensive search for other doped silicon clusters as efficient and more realistic gas-phase catalysts for important dehydrogenation processes in such a way that they can be experimentally prepared and implemented.

Structures, Thermochemical Properties, and Bonding of Mixed Alkaline-Earth-Metal Silicon Trimers Si3M(+/0/-) with M = Be, Mg, Ca.

The ground state geometries, electronic structures, and thermochemical properties of binary alkaline-earth-metal silicon clusters Si3M with M = Be, Mg, Ca in neutral, cationic, and anionic states were investigated using quantum chemical computations. Lowest-lying isomers of the clusters were determined on the basis of the composite G4 energies. Along with total atomization energies, thermochemical parameters were determined for the first time by means of the G4 and coupled-cluster theory with complete basis set CCSD(T)/CBS approaches. The most favored equilibrium formation sequences for Si3M clusters emerge as follows: all Si3M(+/0/-) clusters are formed by attaching the M atom into the corresponding cation, neutral and anion silicon trimer Si3(+/0/-), except for the Si3Mg(+) and Si3Ca(+) where the metal cations are bound to the neutral Si3. The resulting mixed tetramers exhibit geometrical and electronic features similar to those of the pure silicon tetramer Si4(+/0/-). Electron localization function (ELF) and ring current analyses point out that the σ-aromatic character of silicon tetramer remains unchanged upon substituting one Si atom by one alkaline-earth-metal atom.

The role of core–valence electron correlation in gallium halides: a comparison of composite methods

The electronic structure and atomization energies of gas phase gallium halides (GaXn where X = F, Cl, Br, and I, and n = 1 … 3) are studied with highly accurate ab initio composite methods. Coupled cluster methodologies up to full hextuples (CCSDTQPH) are used to compute spectroscopic properties of GaF, which are compared with experiment and conventional levels of theory [such as complete basis set CCSD(T)]. An appropriate treatment of core–valence electron correlation is necessary to obtain reasonable geometries and atomization energies. More efficient composite methods such as the correlation consistent Composite Approach (ccCA, ccCA-TM, rp-ccCA) and the Gaussian-n methods [G3, G3(MP2), G4, G4(MP2)] are calibrated to explore application toward large GaXn-containing molecules relevant to catalysis. For the 12 GaXn compounds, ccCA-TM and rp-ccCA with Boys-localized molecular orbitals has a mean absolute deviation of 1.41 kcal mol−1 compared to complete basis set CCSD(T). However, the G3(MP2) method performs better for complexes with the lighter halides. Calibration of GaXn (X = F, Cl, Br, and I; n = 1–3) ab initio atomization energies is useful to improve prediction of ligand binding energies in novel gallium halide-containing catalysts. Inorganic and organometallic complexes with GaXn ligands are extremely difficult to synthesize and characterize. Therefore, rational design based on well-understood theory is essential.

Molecular structure and spectra of titanium and vanadium trifluorides: Complete basis set CCSD(T) study

Quantum chemical study on TiF3 and VF3 molecules was carried out using the CCSD(T) coupled cluster method using the triple-, quadruple-, and quintuple-zeta basis set and an extrapolation to the complete basis set limit. The methods of multireference configuration interaction MRCISD+Q and perturbation theory MCQDPT2 were used also. The symmetry of the ground electronic state was determined: 2 A′1 and 3 E″ in TiF3 and VF3, respectively. The adiabatic excitation energies were evaluated: AEE(TiF3, \(\tilde A^2 E'' \leftarrow \tilde X^2 A'_1 \)) = 5000 cm−1, AEE(VF3, \(\tilde A^3 A'_2 \leftarrow \tilde X^3 E''\)) = 1000 cm−1. The Jahn-Teller effect in \(\tilde A^2 E''\) state of TiF3 and \(\tilde X^3 E''\) state of VF3 was investigated. The computed Jahn-Teller stabilization energy D 3h → C 2v amounts to 555 and 292 cm−1, respectively. The spin-orbit coupling effect on the VF3 molecular structure and spectrum of electronic states is shown to be quite significant. The calculated vibrational frequencies of TiF3 are in excellent agreement with IR spectroscopy data. The atomization enthalpies were evaluated: Δat H 298 pO = 430 kcal/mol (TiF3), 393 kcal/mol (VF3).

Van der Waals Interaction Energies of Small Fragments of P, As, Sb, S, Se, and Te: Comparison of Complete Basis Set Limit CCSD(T) and DFT with Approximate Dispersion.

Interaction energies of small model van der Waals fragments of group VA (P, As, Sb) and group VIA (S, Se, Te) are calculated using the complete basis set CCSD(T) method and compared to density functional results with approximate treatment of dispersion interaction using vdW-DF- and DFT-D-types of theories. These simple systems show surprising diversity of electronic properties ranging from more "metallic" to more "insulator" like, a property which needs to be captured in the approximate methods. While none of the standard approximate DFT theories provides an entirely satisfactory description of all the systems, we identify the most reliable approaches of each type. In addition, we show that results can be further tuned to chemical accuracy. In vdW-DF theory, guided by physical insights and the availability of quasi-exact CCSD(T) results, we supply the missing parts of correlation by matching an appropriate hybrid/semilocal exchange-correlation functional to describe short-/medium-range correlations accurately. In the DFT-D-type of theories, we reparametrize the empirical dispersion term. Since for such an accurate treatment benchmark calculations are needed, which typically is feasible only for a finite cluster, we argue that the cluster based model of the exchange-correlation hole is transferrable also to extended systems with vdW dispersion interactions.

Approximations to complete basis set-extrapolated, highly correlated non-covalent interaction energies

The first-principles calculation of non-covalent (particularly dispersion) interactions between molecules is a considerable challenge. In this work we studied the binding energies for ten small non-covalently bonded dimers with several combinations of correlation methods (MP2, coupled-cluster single double, coupled-cluster single double (triple) (CCSD(T))), correlation-consistent basis sets (aug-cc-pVXZ, X = D, T, Q), two-point complete basis set energy extrapolations, and counterpoise corrections. For this work, complete basis set results were estimated from averaged counterpoise and non-counterpoise-corrected CCSD(T) binding energies obtained from extrapolations with aug-cc-pVQZ and aug-cc-pVTZ basis sets. It is demonstrated that, in almost all cases, binding energies converge more rapidly to the basis set limit by averaging the counterpoise and non-counterpoise corrected values than by using either counterpoise or non-counterpoise methods alone. Examination of the effect of basis set size and electron correlation shows that the triples contribution to the CCSD(T) binding energies is fairly constant with the basis set size, with a slight underestimation with CCSD(T)∕aug-cc-pVDZ compared to the value at the (estimated) complete basis set limit, and that contributions to the binding energies obtained by MP2 generally overestimate the analogous CCSD(T) contributions. Taking these factors together, we conclude that the binding energies for non-covalently bonded systems can be accurately determined using a composite method that combines CCSD(T)∕aug-cc-pVDZ with energy corrections obtained using basis set extrapolated MP2 (utilizing aug-cc-pVQZ and aug-cc-pVTZ basis sets), if all of the components are obtained by averaging the counterpoise and non-counterpoise energies. With such an approach, binding energies for the set of ten dimers are predicted with a mean absolute deviation of 0.02 kcal/mol, a maximum absolute deviation of 0.05 kcal/mol, and a mean percent absolute deviation of only 1.7%, relative to the (estimated) complete basis set CCSD(T) results. Use of this composite approach to an additional set of eight dimers gave binding energies to within 1% of previously published high-level data. It is also shown that binding within parallel and parallel-crossed conformations of naphthalene dimer is predicted by the composite approach to be 9% greater than that previously reported in the literature. The ability of some recently developed dispersion-corrected density-functional theory methods to predict the binding energies of the set of ten small dimers was also examined.