Basis Set Extrapolation Research Articles

High level ab initio thermochemistry of XeF radical

Thermodynamic characteristics of XeF2 stepwise defluorination reaction have been studied using sophisticated methods of quantum chemistry. The set of standard enthalpies of formation for the XeF2-related intermediates (radicals, ions) was obtained using approximation of coupled clusters level of theory [CCSD(T)/complete basis set extrapolation] with Peterson’s effective core potential correlation consistent basis sets for Xe. The standard enthalpy of formation for xenon monofluoride radical was determined to be ΔfH°(XeF) = 15.4 kcal mol−1 (298 K). The radical is formed in the first step of XeF2 homolytic decomposition which requires 59.7 kcal mol−1. The second step (XeF dissociation) is characterized by an extremely low binding energy (BDE(XeF) = 3.1 kcal mol−1) explaining the high fluorinating potential of the xenon difluoride. An interpretation of low XeF stability was given in terms of MO – AO correlation diagrams. It was shown that the electronic structure of XeF radical may be described as combination of two main configurations, the first of them has a canonical set of MOs with single-occupied HOMO of antibonding character, whereas the second configuration is characterized by low-lying SOMO with main contributions from 5S AO of Xe and 2pz AO of fluorine.

Converged GW quasiparticle energies for transition metal oxide perovskites

The ab initio calculation of quasiparticle (QP) energies is a technically and computationally challenging problem. In condensed matter physics the most widely used approach to determine QP energies is the GW approximation. Although the GW method has been widely applied to many typical semiconductors and insulators, its application to more complex compounds such as transition metal oxide perovskites has been comparatively rare, and its proper use is not well established from a technical point of view. In this work, we have applied the single-shot G0W0 method to a representative set of transition metal oxide perovskites including 3d (SrTiO3, LaScO3, SrMnO3, LaTiO3, LaVO3, LaCrO3, LaMnO3, and LaFeO3), 4d (SrZrO3, SrTcO3, and Ca2RuO4) and 5d (SrHfO3, KTaO3 and NaOsO3) compounds with different electronic configurations, magnetic orderings, structural characteristics and bandgaps ranging from 0.1 to 6.1 eV. We discuss the proper procedure to obtain well converged QP energies and accurate bandgaps within single-shot G0W0 by comparing the conventional approach based on an incremental variation of a specific set of parameters (number of bands, energy cutoff for the plane-wave expansion and number of k-points and the basis-set extrapolation scheme [Phys. Rev. B 90, 075125 (2014)]. In addition, we have inspected the difference between the adoption of norm-conserving and ultrasoft potentials in GW calculations. A minimal statistical analysis indicates that the correlation of the GW data with the DFT gap is more robust than the correlation with the experimental gaps; moreover we identify the static dielectric constant as alternative useful parameter for the approximation of GW gap in high-throughput automatic procedures. Finally, we compute the QP band structure and spectra within the random phase approximation and compare the results with available experimental data.

Straightening the Hierarchical Staircase for Basis Set Extrapolations: A Low-Cost Approach to High-Accuracy Computational Chemistry.

Because the one-electron basis set limit is difficult to reach in correlated post-Hartree-Fock ab initio calculations, the low-cost route of using methods that extrapolate to the estimated basis set limit attracts immediate interest. The situation is somewhat more satisfactory at the Hartree-Fock level because numerical calculation of the energy is often affordable at nearly converged basis set levels. Still, extrapolation schemes for the Hartree-Fock energy are addressed here, although the focus is on the more slowly convergent and computationally demanding correlation energy. Because they are frequently based on the gold-standard coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)], correlated calculations are often affordable only with the smallest basis sets, and hence single-level extrapolations from one raw energy could attain maximum usefulness. This possibility is examined. Whenever possible, this review uses raw data from second-order Møller-Plesset perturbation theory, as well as CCSD, CCSD(T), and multireference configuration interaction methods. Inescapably, the emphasis is on work done by the author's research group. Certain issues in need of further research or review are pinpointed.

Providing theoretical data for detection of four formamidic acid isomers in astrophysical media

We present a theoretical study, so that molecular data (geometrical parameters, vibrational frequencies, infrared intensities, electronic energies, enthalpies, and Gibbs energies) of four formamidic acid (FA) isomers (labeled here as FA1, FA2, FA3, and FA4) and formamide (HCONH2) are obtained from CCSD/cc-pVTZ, CCSD/aug-cc-pVTZ, CCSD/cc-pVQZ, and CCSD(T)/cc-pVTZ calculations. Furthermore, on the basis of insufficient or even lacking theoretical and experimental results in the literature, we employed the aforementioned theory levels to determine benchmark values of dipole moments and rotational constants for these four FA isomers in order to contribute for their detection in astrophysical environments. Besides, we provide for the first time data about forward and reverse rate constants (200–4000 K) and Arrhenius’ parameters for each interconversion reaction between pairs of FA isomers as well as for the tautomeric process involving FA4 and formamide, which were calculated from a Complete Basis Set (CBS) extrapolation equation obtained at CCSD/cc-pVTZ optimized geometries. Our kinetic analysis indicated a faster interconversion between the FA structures in comparison with the FA4 ↔ HCONH2 process, suggesting that these isomers could co-exist in astrophysical media. Finally, we estimated that these isomers may be detected with relative abundances, [FAx]/[HCONH2] (x = 1, 2, 3, and 4), between ∼0.01 and ∼0.1% in astrophysical sources at chemical equilibrium conditions and temperatures around 1000 K. However, these ratios can become as high as ∼1, ∼3, and ∼5%, respectively, in hotter regions with temperatures around 2000, 3000, and 4000 K (expected, for example, in massive star-forming regions).

NMR shielding constants in group 15 trifluorides.

By combining large basis and complete basis set (CBS) extrapolations of the coupled-cluster equilibrium geometry results with rovibrational and relativistic corrections, we demonstrate that it is possible to achieve near-quantitative accuracy for the NMR shielding constants in three group 15 trifluorides - NF3, PF3 and AsF3. These systems provide a rich test set for the calculation of dynamic electron correlation effects on NMR shielding constants. Basis sets as large as aug-cc-pCV6Z were employed, together with coupled-cluster expansion up to CCSDT, at the CCSD(T)/aug-cc-pCVTZ optimised geometries. The results of this work serve to highlight the application of state-of-the-art theoretical techniques which can be employed to guide and supplement NMR experimentation. Combining chemical shifts (either from experiment or high-level calculations) has also enabled a revised reference 19F NMR shielding constant for gas phase CFCl3 to be determined.

Can Popular DFT Approximations and Truncated Coupled Cluster Theory Describe the Potential Energy Surface of the Beryllium Dimer?

The potential energy surface (PES) of the ground state of the beryllium dimer poses a significant challenge for high-level ab initio electronic structure methods. Here, we present a systematic study of basis set effects over the entire PES of Be2 calculated at the full configuration interaction (FCI) level. The reference PES is calculated at the valence FCI/cc-pV{5,6}Z level of theory. We find that the FCI/cc-pV{T,Q}Z basis set extrapolation reproduces the shape of the FCI/cc-pV{5,6}Z PES as well as the binding energy and vibrational transition frequencies to within ~10 cm−1. We also use the FCI/cc-pV{5,6}Z PES to evaluate the performance of truncated coupled cluster methods (CCSD, CCSD(T), CCSDT, and CCSDT(Q)) and contemporary density functional theory methods (DFT) methods for the entire PES of Be2. Of the truncated coupled cluster methods, CCSDT(Q)/cc-pV{5,6}Z provides a good representation of the FCI/cc-pV{5,6}Z PES. The GGA functionals, as well as the HGGA and HMGGA functionals with low percentages of exact exchange tend to severely overbind the Be2 dimer, whereas BH&HLYP and M06-HF tend to underbind it. Range-separated DFT functionals tend to underbind the dimer. Double-hybrid DFT functionals show surprisingly good performance, with DSD-PBEP86 being the best performer. Møller–Plesset perturbation theory converges smoothly up to fourth order; however, fifth-order corrections have practically no effect on the PES.

Guided ion beam and theoretical studies of the bond energy of SmS.

Previous work has shown that atomic samarium cations react with carbonyl sulfide to form SmS+ + CO in an exothermic and barrierless process. To characterize this reaction further, the bond energy of SmS+ is determined in the present study using guided ion beam tandem mass spectrometry. Reactions of SmS+ with Xe, CO, and O2 are examined. Results for collision-induced dissociation processes with all three molecules along with the endothermicity of the SmS+ + CO → Sm+ + COS exchange reaction are combined to yield D0(Sm+-S) = 3.37 ± 0.20 eV. The CO and O2 reactions also yield a SmSO+ product, with measured endothermicities that indicate D0(SSm+-O) = 3.73 ± 0.16 eV and D0(OSm+-S) = 1.38 ± 0.27 eV. The SmS+ bond energy is compared with theoretical values characterized at several levels of theory, including CCSD(T) complete basis set extrapolations using all-electron basis sets. Multireference configuration interaction calculations with explicit spin-orbit calculations along with composite thermochemistry using the Feller-Peterson-Dixon method and all-electron basis sets were also explored for SmS+, and for comparison, SmO, SmO+, and EuO.

On the validity of complete basis set extrapolation formula optimized for the equilibrium distance applied to the potential energy surface for the correlation energy of the helium dimer

AbstractFull configuration interaction calculations are performed for He2 using various orbital basis sets of the aug‐cc‐pVXZ type, with the correlation energies being extrapolated to the complete basis set (CBS) limit. A two‐point CBS extrapolation formula has been utilized for such a purpose. It is shown that the extrapolation formula with the offset parameter k(R) optimized for the equilibrium distance is not uniformly applicable to HeHe distances in the very short region of the potential energy curve. The offset parameter k(R) in the repulsive region of the potential energy curve can be largely different with the one in the long‐range distances especially in the cases of basis‐sets with large cardinality number. It is also noticed that the accuracy of this extrapolation scheme may not be improved with the increasing of the cardinality number.

How To Arrive at Accurate Benchmark Values for Transition Metal Compounds: Computation or Experiment?

With the objective of analyzing which kind of reference data is appropriate for benchmarking quantum chemical approaches for transition metal compounds, we present the following, (a) a collection of 60 transition metal diatomic molecules for which experimentally derived dissociation energies, equilibrium distances, and harmonic vibrational frequencies are known and (b) a composite computational approach based on coupled-cluster theory with basis set extrapolation, inclusion of core-valence correlation, and corrections for relativistic and multireference effects. The latter correction was obtained from internally contracted multireference coupled-cluster (icMRCC) theory. This composite approach has been used to obtain the dissociation energies and spectroscopic constants for the 60 molecules in our data set. In accordance with previous studies on a subset of molecules, we find that multireference corrections are rather small in many cases and CCSD(T) can provide accurate reference values, if the complete basis set limit is explored. In addition, the multireference correction improves the results in cases where CCSD(T) is not a good approximation. For a few cases, however, strong deviations from experiment persist, which cannot be explained by the remaining error in the computational approach. We suggest that these experimentally derived values require careful revision. This also shows that reliable reference values for benchmarking approximate computational methods are not always easily accessible via experiment and accurate computations may provide an alternative way to access them. In order to assess how the choice of reference data affects benchmark studies, we tested 10 DFT functionals for the molecules in the present data set against experimental and calculated reference values. Despite the differences between these two sets of reference values, we found that the ranking of the relative performance of the DFT functionals is nearly independent of the chosen reference.

Accurate Calculations of Rate Constants for the Forward and Reverse H2O + CO ↔ HCOOH Reactions

AbstractThe forward and reverse H2O + CO ↔ HCOOH reactions were investigated using high‐level methodologies in order to provide accurate thermodynamic and kinetic data between 200 and 4000 K. Geometries of reactants, transition state (TS), and product were determined with the Coupled Cluster Theory including single and double excitations (CCSD) along with the cc‐pVTZ basis set, whereas associated vibrational frequencies, zero‐point energies, and thermal corrections were scaled to consider anharmonicity effects. Besides, the description of electronic energies was improved by means of core‐valence correlation and iterative triple‐excitation contributions together with a complete basis set extrapolation (ECBS,Δ) in order to achieve accurate values of enthalpies, Gibbs energies, and rate constants. Such rate constants were estimated at the high‐pressure limit by variational TS treatments combined with different quantum tunneling approaches. Finally, modified Arrhenius’ equations were fitted between 700 and 4000 K from our most reliable results.

Ionization of pyridine: Interplay of orbital relaxation and electron correlation.

The valence shell ionization spectrum of pyridine was studied using the third-order algebraic-diagrammatic construction approximation scheme for the one-particle Green's function and the outer-valence Green's function method. The results were used to interpret angle resolved photoelectron spectra recorded with synchrotron radiation in the photon energy range of 17-120 eV. The lowest four states of the pyridine radical cation, namely, 2A2(1a2-1), 2A1(7a1-1), 2B1(2b1-1), and 2B2(5b2-1), were studied in detail using various high-level electronic structure calculation methods. The vertical ionization energies were established using the equation-of-motion coupled-cluster approach with single, double, and triple excitations (EOM-IP-CCSDT) and the complete basis set extrapolation technique. Further interpretation of the electronic structure results was accomplished using Dyson orbitals, electron density difference plots, and a second-order perturbation theory treatment for the relaxation energy. Strong orbital relaxation and electron correlation effects were shown to accompany ionization of the 7a1 orbital, which formally represents the nonbonding σ-type nitrogen lone-pair (nσ) orbital. The theoretical work establishes the important roles of the π-system (π-π* excitations) in the screening of the nσ-hole and of the relaxation of the molecular orbitals in the formation of the 7a1(nσ)-1 state. Equilibrium geometric parameters were computed using the MP2 (second-order Møller-Plesset perturbation theory) and CCSD methods, and the harmonic vibrational frequencies were obtained at the MP2 level of theory for the lowest three cation states. The results were used to estimate the adiabatic 0-0 ionization energies, which were then compared to the available experimental and theoretical data. Photoelectron anisotropy parameters and photoionization partial cross sections, derived from the experimental spectra, were compared to predictions obtained with the continuum multiple scattering approach.

Communication: A novel implementation to compute MP2 correlation energies without basis set superposition errors and complete basis set extrapolation.

By using a formulation based on the dynamical polarizability, we propose a novel implementation of second-order Møller-Plesset perturbation (MP2) theory within a plane wave (PW) basis set. Because of the intrinsic properties of PWs, this method is not affected by basis set superposition errors. Additionally, results are converged without relying on complete basis set extrapolation techniques; this is achieved by using the eigenvectors of the static polarizability as an auxiliary basis set to compactly and accurately represent the response functions involved in the MP2 equations. Summations over the large number of virtual states are avoided by using a formalism inspired by density functional perturbation theory, and the Lanczos algorithm is used to include dynamical effects. To demonstrate this method, applications to three weakly interacting dimers are presented.

High-level ab initio studies of the complex formed between CO and O2

The explicitly correlated CCSD(T)-F12 method with VXZ-F12 basis sets was used to find the most stable structures of the van der Waals CO-O2 complexes. With geometry optimizations performed up to the quadruple-zeta level and basis set extrapolation, the calculated interaction energies for the triplet complexes are 123cm−1 for the H complex in Cs symmetry (slipped near-parallel structure), 118cm−1 for the X complex, also in Cs symmetry (perpendicular alignment) and 116cm−1 for the CO-O2 T complex in C2v symmetry. The corresponding CCSD(T)-F12 results using the aug-cc-pVXZ basis sets are nearly the same. Similar calculations were performed for the CO-O2 singlet complexes, which are shown to have much higher stabilization energies, the highest being 206cm−1 for the X complex.

Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis.

We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O(N4), with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.

On the performance of an complete basis set extrapolation scheme tailored for the equilibrium distance applied to the helium dimer potential energy surface

Full configuration interaction calculations are performed for He2 using various orbital basis sets of the aug-cc-pVXZ type, with the results being extrapolated to the one electron basis set limit both with counterpoise and without counterpoise correction. A two-point complete basis set extrapolation formula optimized for the equilibrium distance has been utilized for such a purpose. The results call into question the use of the extrapolation formula tailored for the equilibrium distance at other points on the potential surface.

GW100: A Plane Wave Perspective for Small Molecules.

In a recent work, van Setten and co-workers have presented a carefully converged G0W0 study of 100 closed shell molecules [ J. Chem. Theory Comput. 2015 , 11 , 5665 - 5687 ]. For two different codes they found excellent agreement to within a few 10 meV if identical Gaussian basis sets were used. We inspect the same set of molecules using the projector augmented wave method and the Vienna ab initio simulation package (VASP). For the ionization potential, the basis set extrapolated plane wave results agree very well with the Gaussian basis sets, often reaching better than 50 meV agreement. In order to achieve this agreement, we correct for finite basis set errors as well as errors introduced by periodically repeated images. For positive electron affinities differences between Gaussian basis sets and VASP are slightly larger. We attribute this to larger basis set extrapolation errors for the Gaussian basis sets. For quasi particle (QP) resonances above the vacuum level, differences between VASP and Gaussian basis sets are, however, found to be substantial. This is tentatively explained by insufficient basis set convergence of the Gaussian type orbital calculations as exemplified for selected test cases.

Accurate spectroscopic calculations of the 22 Λ-S states and 60 Ω states of the PS+ cation

This work studied the potential energy curves of 22 Λ-S states, which were yielded from the first two dissociation limits, P(4Su)+S+(4Su) and P+(3Pg)+S(3Pg), of the PS+ cation. The potential energy curves were calculated employing the CASSCF method, which was followed by the internally contracted MRCI approach with Davidson correction. Core- valence correlation and scalar relativistic corrections as well as basis set extrapolation were included. Of these 22 Λ-S states, only the 35Σ+ state was repluse without the spin-orbit coupling effect, whereas the 35Σ+, 15Δ, 25Σ+, and 15Σ− states were repulse with the spin-orbit coupling effect accounted for. The 21Π and 23Π states had double wells, but the first well of the 23Π state had no vibrational levels and the first well of 21Π state had only one vibrational state. The avoided crossings were found between the 11Π and 21Π states and between the d3Π and 23Π states. The 25Σ+, 15Π, 15Δ, b3Δ, and c3Σ− states were inverted with the spin-orbit coupling effect taken into account. The 15Δ, 25Σ+, 15Σ−, and 21Π states were weakly bound. The spectroscopic properties were evaluated and compared with the experimental and other theoretical results. The Franck-Condon factors of some electronic transitions between different Λ-S states were determined. The vibrational levels of several states were predicted. The spin-orbit coupling effect on the spectroscopic parameters was discussed. Analyses show that the spectroscopic results obtained here can be expected to be reliably predicted ones.

Theoretical Study of the Ti–Cl Bond Cleavage Reaction in TiCl4

Abstract In this work the kinetics of the TiCl4 ⇌ TiCl3 + Cl reaction is studied theoretically. A variable-reaction coordinate transition-state theory (VRC-TST) is used to calculate the high-pressure limit rate coefficients. The interaction energy surface for the VRC-TST step is sampled directly at the CASPT2(6e,4o)/cc-pVDZ level of theory including an approximate treatment of the spin-orbit coupling. The pressure-dependence of the reaction in an argon bath gas is explored using the master equation in conjunction with the optimised VRC-TST transition-state number of states. The collisional energy transfer parameters for the TiCl4–Ar system are estimated via a “one-dimensional minimisation” method and classical trajectories. The Ti–Cl bond dissociation energy is computed using a complete basis set extrapolation technique with cc-pVQZ and cc-pV5Z basis sets. Good quantitative agreement between the estimated rate constants and available literature data is observed. However, the fall-off behaviour of the model results is not seen in the current experimental data. Sensitivity analysis shows that the fall-off effect is insensitive to the choice of model parameters and methods. More experimental work and development of higher-level theoretical methods are needed to further investigate this discrepancy.

Accurate spectroscopic calculations of the 19 Λ-S states and 36 Ω states of the BC+ cation

ABSTRACTThis work computed the potential energy curves of 19 Λ-S states, which arose from the first five dissociation limits of BC+ cation, B+(1Sg) + C(3Pg), B+(1Sg) + C(1Dg), B+(1Sg) + C(1Sg), C+(2Pu) + B(2Pu), and B+(1Sg) + C(5Su). The calculations were done for internuclear separations from 0.08 to 1.07 nm. The potential energy curves of 36 Ω states yielded from these Λ-S states were also calculated. Core-valence correlation and scalar relativistic correction, basis set extrapolation as well as Davidson correction were accounted for. Of these Λ-S states, the c1Σ+, D3Π, 21Π, 23Σ+, 21Δ, 31Σ+, and 41Σ+ had double wells; the 33Π and 31Π states had three wells; the C3Σ− and D3Π states were inverted with the spin-orbit coupling effect included; and the second wells of c1Σ+, D3Π and 31Σ+ states, the second and the third wells of 33Π state as well as the third well of 31Π state were very weakly bound, which well depths were smaller than 400 cm−1. The spectroscopic parameters were determined for all the states. The vibrational properties were predicted only for some weakly bound states. The spin-orbit coupling effect on the spectroscopic parameters was evaluated.

On the complete basis set extrapolation procedures for the interaction energies

In the present contribution, it is shown that the two-point extrapolation of the interaction energies towards the complete basis set limit with the total interaction energies extrapolated directly shows comparable accuracy to the extrapolation scheme in which the Hartree-Fock and correlation energies components of the total interaction energies are extrapolated separately. It is also found that better accuracy is achieved when energy values without the counterpoise correction are used in the extrapolation procedure. Accordingly, it may be recommended to extrapolate the total interaction energies without counterpoise correction directly to approximate the complete basis set results. These results are based on full CI calculations of He2 with the aug-cc-pVXZ (X=T, Q, 5) basis sets.