Basis Set Limit Extrapolation Research Articles

ExoMol line lists – LIII: empirical rovibronic spectra of yttrium oxide

ABSTRACT Empirical line lists BRYTS for the open shell molecule 89Y16O (yttrium oxide) and its isotopologues are presented. The line lists cover the six lowest electronic states: $X\, {}^{2}\Sigma ^{+}$, $A\, {}^{2}\Pi$, $A^{\prime }\, {}^{2}\Delta$, $B\, {}^{2}\Sigma ^{+}$, $C\, {}^{2}\Pi$, and $D\, {}^{2}\Sigma ^{+}$ up to 60 000 cm−1 (<0.167 $\mu$m) for rotational excitation up to J = 400.5. An ab initio spectroscopic model consisting of potential energy curves (PECs), spin–orbit, and electronic angular momentum couplings is refined by fitting to experimentally determined energies of YO, derived from published YO experimental transition frequency data. The model is complemented by empirical spin-rotation and Λ-doubling curves and ab initio dipole moment and transition dipole moment curves computed using multireference configuration interaction (MRCI). The ab initio PECs computed using the complete basis set limit extrapolation and the coupled-cluster CCSD(T) method with its higher quality provide an excellent initial approximation for the refinement. Non-adiabatic coupling curves for two pairs of states of the same symmetry A/C and B/D are computed using a state-averaged complete active space self-consistant field theory (CASSCF) and used to build diabatic representations for the $A\, {}^{2}\Pi$, $C\, {}^{2}\Pi$, $B\, {}^{2}\Sigma ^{+}$, and $D\, {}^{2}\Sigma ^{+}$ curves. The experimentally derived energies of 89Y16O utilized in the fit are used to replace the corresponding calculated energy values in the BRYTS line list. Simulated spectra of YO show excellent agreement with the experiment, where it is available. Calculated lifetimes of YO are tuned to agree well with the experiment, where available. The BRYTS YO line lists are available from the ExoMol database (www.exomol.com).

Multicomponent wavefunction-in-DFT embedding for positronium molecules.

This work presents an extension of the projector operator embedding scheme of Manby et al. [J. Chem. Theory Comput. 8, 2564 (2012)] in a multicomponent (MC) framework. Here, a molecular system containing electrons and other types of quantum species is divided into a wavefunction (WF) subsystem of interest and a density functional theory (DFT) environment. The WF-in-DFT partition decreases computational costs by partially truncating the WF subsystem basis set at the cost of introducing a controllable embedding error. To explore the applicability of the MC extension, third-order propagator-in-DFT calculations were performed for positron-anion complexes for alkoxides and carboxylates with carbon chains of different sizes. For these systems, it was found that selecting a WF subsystem with the positron and only the oxygen atoms caused an error of 0.1eV or lower in positron-binding energies, while reducing between 33% and 55% the basis set size. The reduction of computational costs achieved with the embedding scheme allowed us to improve molecular positron-binding energy predictions by performing complete basis set limit extrapolations. Combining the WF-in-DFT embedding and the complete basis set extrapolation, positronium aliphatic alkoxides were predicted to be energetically stable by 0.3eV with respect to Ps emission. Similarly, positronium carboxylates, both aromatic and aliphatic, were predicted to be stable by 1.3eV.

A theoretical study of the photoelectron spectra of dichloroketene with accurate computation of ionization energies via complete basis set limit extrapolation

AbstractWe calculated the equilibrium geometries and harmonic vibrational frequencies of the ground state and five cationic states of dichloroketene using (TD‐)B3LYP, PBE0, and M06/M06‐2X approaches. The photoelectron spectra of dichloroketene were simulated by computing Franck‐Condon factors. The ionization energies were computed using the CCSD(T) approach with extrapolation to the complete basis set (CBS) limit. We propose two new CBS energy formulas (E = ECBS + Aexp(‐x) + B/(x−1) n, n = 2 or 3) and compare the performance of different CBS approaches. A new ionic state of dichloroketene belonging to the Cs point group is reported. This state is identified as the first excited state of Cl2CCO+ having a double‐well potential‐energy curve along the CCO bending mode with a barrier height of 1.335 eV. The simulated photoelectron spectra are in agreement with the experiment. The vertical ionization energies calculated via spectral simulation are more accurate compared with those obtained at the ground‐state structure. Among the CBS formulas used, the proposed ansatz with n = 2 performs best, with a mean absolute error of 0.021 and 0.012 eV for the adiabatic and vertical ionization energies, respectively.

Anion Photoelectron Spectroscopy and High Level Ab Initio Calculations of the Halide–Nitric Oxide Dimer Complexes

Anion photoelectron spectra are presented for gas phase complexes formed between halide anions and nitric oxide, X−⋯NO where X− = Cl−, Br−, and I−. Electron binding energies are experimentally determined to be 3.82, 3.51, and 3.17 eV. Results from CCSD(T)/aug-cc-pVTZ calculations are presented for the anion species, whereby a single minimum of Cs symmetry is predicted. Binding energies (D0) of 15.3, 13.3, and 11.7 kJ mol−1 are predicted from complete basis set limit extrapolation, and are found to be in line with previous experimental studies.

Towards a quantum chemical protocol for the prediction of rovibrational spectroscopic data for transition metal molecules: Exploration of CuCN, CuOH, and CuCCH.

High accuracy electronic structure computations for small transition metal-containing molecules have been a long term challenge. Due to coupling between electronic and nuclear wave functions, even experimental/theoretical identification of the ground electronic state requires tremendous efforts. Quartic force fields (QFFs) are effective ab initio tools for obtaining reliable anharmonic spectroscopic properties. However, the method that employs complete basis set limit extrapolation ("C"), consideration of core electron correlation ("cC"), and inclusion of scalar relativity ("R") to produce the energy points on the QFF, the composite CcCR methodology, has not yet been utilized to study inorganic spectroscopy. This work takes the CcCR methodology and adapts it to test whether such an approach is conducive for the closed-shell, copper-containing molecules CuCN, CuOH, and CuCCH. Gas phase rovibrational data are provided for all three species in their ground electronic states. Equilibrium geometries and many higher-order rovibrational properties show good agreement with earlier studies. However, there are notable differences, especially in computation of fundamental vibrational frequencies. Even with further additive corrections for the inner core electron correlation and coupled cluster with full single, double, and triple substitutions (CCSDT), the differences are still larger than expected indicating that more work should follow for predicting rovibrational properties of transition metal molecules.

Estimating the intrinsic limit of the Feller-Peterson-Dixon composite approach when applied to adiabatic ionization potentials in atoms and small molecules

Benchmark adiabatic ionization potentials were obtained with the Feller-Peterson-Dixon (FPD) theoretical method for a collection of 48 atoms and small molecules. In previous studies, the FPD method demonstrated an ability to predict atomization energies (heats of formation) and electron affinities well within a 95% confidence level of ±1 kcal/mol. Large 1-particle expansions involving correlation consistent basis sets (up to aug-cc-pV8Z in many cases and aug-cc-pV9Z for some atoms) were chosen for the valence CCSD(T) starting point calculations. Despite their cost, these large basis sets were chosen in order to help minimize the residual basis set truncation error and reduce dependence on approximate basis set limit extrapolation formulas. The complementary n-particle expansion included higher order CCSDT, CCSDTQ, or CCSDTQ5 (coupled cluster theory with iterative triple, quadruple, and quintuple excitations) corrections. For all of the chemical systems examined here, it was also possible to either perform explicit full configuration interaction (CI) calculations or to otherwise estimate the full CI limit. Additionally, corrections associated with core/valence correlation, scalar relativity, anharmonic zero point vibrational energies, non-adiabatic effects, and other minor factors were considered. The root mean square deviation with respect to experiment for the ionization potentials was 0.21 kcal/mol (0.009 eV). The corresponding level of agreement for molecular enthalpies of formation was 0.37 kcal/mol and for electron affinities 0.20 kcal/mol. Similar good agreement with experiment was found in the case of molecular structures and harmonic frequencies. Overall, the combination of energetic, structural, and vibrational data (655 comparisons) reflects the consistent ability of the FPD method to achieve close agreement with experiment for small molecules using the level of theory applied in this study.

Efficient yet accurate approximations for ab initio calculations of alcohol cluster thermochemistry.

We have calculated the binding enthalpies and entropies of gas phase alcohol clusters from ethanol to 1-decanol. In addition to the monomers, we have investigated dimers, tetramers, and pentamers. Geometries have been obtained at the B3LYP/TZVP level and single point energy calculations have been performed with the Resolution of the Identity-MP2 (RIMP2) method and basis set limit extrapolation using aug-cc-pVTZ and aug-cc-pVQZ basis sets. Thermochemistry is calculated with decoupled hindered rotor treatment for large amplitude motions. The results show three points: First, it is more accurate to transfer the rigid-rotor harmonic oscillator entropies from propanol to longer alcohols than to compute them with an ultra-fine grid and tight geometry convergence criteria. Second, the computational effort can be reduced considerably by using dimerization energies of longer alcohols at density functional theory (B3LYP) level plus a RIMP2 correction obtained from 1-propanol. This approximation yields results almost with the same accuracy as RIMP2 - both methods differ for 1-decanol only 0.4 kJ/mol. Third, the entropy of dimerization including the hindered rotation contribution is converged at 1-propanol with respect to chain length. This allows for a transfer of hindered rotation contributions from smaller alcohols to longer ones which reduces the required computational and man power considerably.

On the validity of the basis set superposition error and complete basis set limit extrapolations for the binding energy of the formic acid dimer.

We report the variation of the binding energy of the Formic Acid Dimer with the size of the basis set at the Coupled Cluster with iterative Singles, Doubles and perturbatively connected Triple replacements [CCSD(T)] level of theory, estimate the Complete Basis Set (CBS) limit, and examine the validity of the Basis Set Superposition Error (BSSE)-correction for this quantity that was previously challenged by Kalescky, Kraka, and Cremer (KKC) [J. Chem. Phys. 140, 084315 (2014)]. Our results indicate that the BSSE correction, including terms that account for the substantial geometry change of the monomers due to the formation of two strong hydrogen bonds in the dimer, is indeed valid for obtaining accurate estimates for the binding energy of this system as it exhibits the expected decrease with increasing basis set size. We attribute the discrepancy between our current results and those of KKC to their use of a valence basis set in conjunction with the correlation of all electrons (i.e., including the 1s of C and O). We further show that the use of a core-valence set in conjunction with all electron correlation converges faster to the CBS limit as the BSSE correction is less than half than the valence electron/valence basis set case. The uncorrected and BSSE-corrected binding energies were found to produce the same (within 0.1 kcal/mol) CBS limits. We obtain CCSD(T)/CBS best estimates for De = - 16.1 ± 0.1 kcal/mol and for D0 = - 14.3 ± 0.1 kcal/mol, the later in excellent agreement with the experimental value of -14.22 ± 0.12 kcal/mol.

Ab initio potential energy surface for methane and carbon dioxide and application to vapor-liquid coexistence.

A six-dimensional intermolecular potential energy surface for a rigid methane (CH4) and carbon dioxide (CO2) dimer was developed from the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory. A total of 466 grid points distributed to 46 orientations were calculated from the complete basis set limit extrapolation based on up to aug-cc-pVQZ basis set. A modified site-site pair potential function was proposed for rapid representation of the high level ab initio calculations. A nonadditive three-body interaction was represented by the Axilrod-Teller-Muto expression for mixtures with the polarizability and the London dispersion constant of each molecule. Second to fourth virial coefficients of CH4 and CO2 mixtures were calculated using both the Mayer sampling Monte Carlo method and the present potential functions. The virial equation of state derived from these coefficients was used to predict the pVT values and showed good agreement with experimental data below 200 bar at 300 K. The vapor-liquid coexistence curves of pure CH4, CO2 and their mixtures were presented with the aid of Gibbs ensemble Monte Carlo simulations. The predicted tie lines agreed with the experimental data within the uncertainties up to near the critical point.

A high-accuracy theoretical study of the CHnP Systemsn = 1-3

We have performed high-level electronic structure computations on the most important species of the CH(n)P systems n = 1-3 to characterize them and provide reliable information about the equilibrium and vibrationally averaged molecular structures, rotational constants, vibrational frequencies (harmonic and anharmonic), formation enthalpies, and vertical excitation energies. Those chemical systems are intermediates for several important reactions and also prototypical phosphorus-carbon compounds; however, they are often elusive to experimental detection. The present results significantly complement their knowledge and can be used as an assessment of the experimental information when available. The explicitly correlated coupled-cluster RCCSD(T)-F12 method has been used for geometry optimizations and vibrational frequency calculations. Vibrational configuration interaction theory has been used to account for anharmonicity effects. Basis-set limit extrapolations have been carried out to determine accurate thermochemical quantities. Electronic excited states have been calculated with coupled-cluster approaches and also by means of the multireference configuration interaction method.

Experimental and computational investigation of the group 11–group 2 diatomic molecules: First determination of the AuSr and AuBa bond energies and thermodynamic stability of the copper- and silver-alkaline earth species

The dissociation energies of the intermetallic molecules AuSr and AuBa were for the first time determined by the Knudsen effusion mass spectrometry method. The two species were produced in the vapor phase equilibrated with apt mixtures of the constituent elements, and the dissociation equilibria were monitored mass-spectrometrically in the temperature range 1406-1971 K (AuSr) and 1505-1971 K (AuBa). The third-law analysis of the equilibrium data gives the following dissociation energies (D(0)°, in kJ/mol): 244.4 ± 4.8 (AuSr) and 273.3 ± 6.3 (AuBa), so completing the series of D(0)°s for the AuAE (AE = group 2 element) diatomics. The AuAE species were also studied computationally at the coupled cluster including single, double and perturbative triple excitation [CCSD(T)] level with basis sets of increasing zeta quality, and various complete basis set limit extrapolations were performed to calculate the dissociation energies. Furthermore, the entire series of the heteronuclear diatomic species formed from one group 11 (Cu, Ag) and one group 2 (Be, Mg, Ca, Sr, Ba) metal was studied by DFT with the hybrid meta-GGA TPSSh functional and the def2-QZVPP basis set, selected after screening a number of functional-basis set combinations using the AuAE species as benchmark. Dissociation energies, internuclear distances, vibrational frequencies, and anharmonic constants were determined for the CuAE and AgAE species and their thermal functions evaluated therefrom. On this basis, a thermodynamic evaluation of the formation of these species was carried out under various conditions.

Complete basis set limit extrapolation calculations with PNOF3

Complete basis set (CBS) extrapolated total energies have been calculated for the ground state and lowest-lying excited state with different spin of the second-row atoms (Li–Ne) using the recently developed spin-conserving PNOF3 natural orbital functional. CBS results are obtained by extrapolating power and exponential functions to the results obtained using the correlation-consistent aug-cc-pVTZ, aug-cc-pVQZ and aug-cc-pV5Z basis sets. The extrapolated total energy values are very accurate as compared to the benchmark data, and reproduce near 100% of the total energy. Interestingly, the benchmark data are lower bounds for the PNOF3 results. Finally, we have found that the calculated PNOF3 excitation energies are very accurate as comparing with both their corresponding CCSD(T, full) values and their experimental marks.

H2O, H2, HF, F2 and F2O nuclear magnetic shielding constants and indirect nuclear spin–spin coupling constants (SSCCs) in the BHandH/pcJ‐n and BHandH/XZP Kohn–Sham limits

Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H(2)O, H(2), HF, F(2) and F(2)O nuclear isotropic shielding constants in the BHandH Kohn-Sham basis set limit was shown. The results of two- and three-parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization-consistent basis sets pcS-n and pcJ-n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were more sensitive to the XZP basis set size and generally less accurate than those estimated using pcJ-n basis set family. The BHandH density functional markedly outperforms B3LYP method in predicting heavy atom shieldings and SSCCs values in the studied systems.

Ab Initio and Density Functional Theory Reinvestigation of Gas-Phase Sulfuric Acid Monohydrate and Ammonium Hydrogen Sulfate

We have calculated the thermochemical parameters for the reactions H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O and H(2)SO(4) + NH(3) <--> H(2)SO(4).NH(3) using the B3LYP and PW91 functionals, MP2 perturbation theory and four different basis sets. Different methods and basis sets yield very different results with respect to, for example, the reaction free energies. A large part, but not all, of these differences are caused by basis set superposition error (BSSE), which is on the order of 1-3 kcal mol(-1) for most method/basis set combinations used in previous studies. Complete basis set extrapolation (CBS) calculations using the cc-pV(X+d)Z and aug-cc-pV(X+d)Z basis sets (with X = D, T, Q) at the B3LYP level indicate that if BSSE errors of less than 0.2 kcal mol(-1) are desired in uncorrected calculations, basis sets of at least aug-cc-pV(T+d)Z quality should be used. The use of additional augmented basis functions is also shown to be important, as the BSSE error is significant for the nonaugmented basis sets even at the quadruple-zeta level. The effect of anharmonic corrections to the zero-point energies and thermal contributions to the free energy are shown to be around 0.4 kcal mol(-1) for the H(2)SO(4).H(2)O cluster at 298 K. Single-point CCSD(T) calculations for the H(2)SO(4).H(2)O cluster also indicate that B3LYP and MP2 calculations reproduce the CCSD(T) energies well, whereas the PW91 results are significantly overbinding. However, basis-set limit extrapolations at the CCSD(T) level indicate that the B3LYP binding energies are too low by ca. 1-2 kcal/mol. This probably explains the difference of about 2 kcal mol(-1) for the free energy of the H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O reaction between the counterpoise-corrected B3LYP calculations with large basis sets and the diffusion-based experimental values of S. M. Ball, D. R. Hanson, F. L Eisele and P. H. McMurry (J. Phys. Chem. A. 2000, 104, 1715). Topological analysis of the electronic charge density based on the quantum theory of atoms in molecules (QTAIM) shows that different method/basis set combinations lead to qualitatively different bonding patterns for the H(2)SO(4).NH(3) cluster. Using QTAIM analysis, we have also defined a proton transfer degree parameter which may be useful in further studies.

An ab initio study of trans-1-chloro-2-fluoroethylene: Equilibrium structure and molecular properties

The equilibrium structure and molecular properties of trans-1-chloro-2-fluoroethylene have been investigated theoretically at high level of theory. Very accurate results are presented. As far as the equilibrium structure is concerned, coupled-cluster approach with perturbative inclusion of triples and basis sets of triple and quadruple zeta quality have been employed. Core correlation effects and basis set limit extrapolation have been taken into account in order to obtain best estimates of equilibrium geometry. The molecular dipole moment has been calculated at coupled-cluster level using bases of different quality including diffuse functions and performing the extrapolation to the infinite basis set limit. In addition, the complete inertial nuclear quadrupole tensor, evaluated from the electric field gradient at the chlorine nucleus, has been computed at different level of theory: The multiconfiguration self-consistent field, the Møller–Plesset many-body perturbation to second order and the coupled-cluster methods have been employed. Finally, the harmonic force field has been calculated by means of coupled-cluster approach with a basis of triple zeta quality.

Basis set limit extrapolation of ACPF and CCSD(T) results for the third and fourth lanthanide ionization potentials

Theoretical values for the third and fourth ionization potentials of the lanthanide elements from La to Lu are presented. The results are based on large-scale multi-reference averaged coupled-pair functional calculations starting from a complete active space reference wavefunction and single-reference coupled-cluster calculations. Relativistic effects were accounted for by small-core energy-consistent ab initio pseudopotentials. The results obtained for optimized uncontracted valence basis sets including up to i functions were extrapolated to the basis set limit. The importance of higher angular momentum basis functions in ab initio calculations for energy differences between configurations with different 4f occupation numbers is discussed.