Basis Set Effects Research Articles

Benchmarking quantum mechanical methods for calculating reaction energies of reactions catalyzed by enzymes

To assess the accuracy of different quantum mechanical methods for biochemical modeling, the reaction energies of 20 small model reactions (chosen to represent chemical steps catalyzed by commonly studied enzymes) were calculated. The methods tested included several popular Density Functional Theory (DFT) functionals, second-order Møller Plesset perturbation theory (MP2) and its spin-component scaled variant (SCS-MP2), and coupled cluster singles and doubles and perturbative triples (CCSD(T)). Different basis sets were tested. CCSD(T)/aug-cc-pVTZ results for all 20 reactions were used to benchmark the other methods. It was found that MP2 and SCS-MP2 reaction energy calculation results are similar in quality to CCSD(T) (mean absolute error (MAE) of 1.2 and 1.3 kcal mol−1, respectively). MP2 calculations gave a large error in one case, and are more subject to basis set effects, so in general SCS-MP2 calculations are a good choice when CCSD(T) calculations are not feasible. Results with different DFT functionals were of reasonably good quality (MAEs of 2.5–5.1 kcal mol−1), whereas popular semi-empirical methods (AM1, PM3, SCC-DFTB) gave much larger errors (MAEs of 11.6–14.6 kcal mol−1). These results should be useful in guiding methodological choices and assessing the accuracy of QM/MM calculations on enzyme-catalyzed reactions.

Hetero-site Double Core Ionization Energies with Sub-electronvolt Accuracy from Delta-Coupled-Cluster Calculations.

Benchmark scalar-relativistic delta-coupled-cluster calculations of hetero-site double core ionization energies of small molecules containing second-row elements are reported. The present study has focused on the high-spin triplet components of two-site double core-ionized states, which are single reference in character and consistent with the use of standard coupled-cluster methods. Contributions to computed double core ionization energies from electron-correlation and basis-set effects as well as corrections to the core-valence separation approximation have been analyzed. On the basis of systematic convergence of computational results with respect to these effects, delta-coupled-cluster calculations have been shown to be capable of providing accurate double core ionization energies with remaining errors estimated to be below 0.3 eV, and thus they are recommended for use to facilitate experimental studies of two-site double core-ionized states that are involved in X-ray pump/X-ray probe studies of electronic and molecular dynamics following inner shell ionization or excitation.

Hyperfine Structure Constants on the Relativistic Coupled Cluster Level with Associated Uncertainties.

Accurate predictions of hyperfine structure (HFS) constants are important in many areas of chemistry and physics, from the determination of nuclear electric and magnetic moments to benchmarking of new theoretical methods. We present a detailed investigation of the performance of the relativistic coupled cluster method for calculating HFS constants within the finite-field scheme. The two selected test systems are 133Cs and 137BaF. Special attention has been paid to construct a theoretical uncertainty estimate based on investigations on basis set, electron correlation and relativistic effects. The largest contribution to the uncertainty estimate comes from higher order correlation contributions. Our conservative uncertainty estimate for the calculated HFS constants is ∼5.5%, while the actual deviation of our results from experimental values is <1% in all cases.

Time-Dependent Density Functional Theory Investigation of the UV–Vis Spectra of Organonitrogen Chromophores in Brown Carbon

The ability of brown carbon (BrC) in aerosols to absorb solar radiation is an important but highly uncertain factor in climate forcing. The uncertainties are partially due to incomplete characterization of BrC chromophores and lack of authentic standards to confirm light absorption. Organonitrogen species are crucial components in atmospheric aerosols, but their light-absorbing properties remain to be fully characterized. To facilitate the molecular characterization of BrC chromophores, time-dependent density functional theory (TD-DFT) based computational chemistry approaches were used in this study to predict the light absorption spectra of 16 organonitrogen species, including nitroaromatics, nitro-heterocyclic compounds, organonitrates, and Maillard-type reaction products in BrC. Effects of basis sets, functionals, solvation, and pH on light absorption properties of these compounds were evaluated. Predicted absorption spectra were compared with experimental measurements. Overall, the PBE0 and B3LYP functionals tend to outperform PBE and CAM-B3LYP on the predicted absorption spectra of studied compounds. Absorbance calculated in water and methanol (bulk solvents) varies up to 2 nm (0.03 eV). Absorbance calculated in gas phase (vacuum state) blue-shifts in comparison to solvation. Absorbance of weak acids (e.g., nitrophenols) is enhanced under basic conditions, and the absorption spectra can be predicted by the fractions of conjugate acid–base species. Results from this study demonstrate that a combined use of TD-DFT predictions and experimental measurements of light absorption can allow for a rapid and reliable determination of potential chromophores in BrC when authentic standards are not available.

The Effect of Basis Set on Quantum Tunneling Probability with the Case of trans-HCOH Isomerization

We investigate the effects of basis set in quantum tunneling probability in the case of trans-HCOH isomerization to H2CO. Based on Density Functional Theory (DFT) calculation with B3LYP as functional exchange-correlation and 6-31G(d, p) as basis set, Rizka et al. found that trans-HCOH molecule has half life for 2.5 hours. The result has 0.7 hour longer than experimental result done by Schreiner et al. In this study, we used five variations of basis set which are: STO-3G, 6-31G, 6-31G(d, p), 6-31+G(d, p), and LANL2DZ. We started to investigate the effects of basis set on the electronic structure and vibrational frequency of the molecules. Then, we investigated the effects of basis set on quantum tunneling probability in molecule. Based on quantum tunneling probabilities, we could calculate half-life of trans-HCOH isomerization to H2CO. We compare our results to the experimental result done by Schreiner et al. The results show that basis set increases the quantum tunneling probability of the isomerization.

Role of Augmented Basis Sets and Quest for ab Initio Performance/Cost Alternative to Kohn-Sham Density Functional Theory.

Following a previous work, we have assessed the feasibility of MP2/CBS(d, t) as an alternative to state-of-the-art density functionals. The effect of using augmented basis sets is here tested on the 76 barrier heights and 10 isomerization reactions previously utilized. Moreover, calculations for 20 sets of the GMTKN24 database for thermochemistry, kinetics, and noncovalent interactions have been performed. For the density functional theory calculations, M06-2X and B3LYP-D3 functionals are utilized as two representative functionals, while MP2 and CCSD(T) methods are employed as the ab initio counterparts. The results show that MP2 calculations perform similarly to the ones obtained with M06-2X insofar as accuracy and computational cost are concerned. For all methods, the use of augmented basis sets yields enhanced results for anionic systems when compared with the ones from non-augmented bases. Otherwise, the basis-set change effect is found to be minimal. It is therefore concluded that the use of large basis sets is unjustified when facing the increase in computational cost.

Phosphorus mononitride: A difficult case for theory

AbstractPhosphorus nitride (PN) is the simplest molecule formed solely by phosphorus and nitrogen. It represents an interesting model for materials, where phosphorus is directly attached to nitrogen. Nevertheless, both theoretical and experimental studies often provide an incomplete picture on the structural, electronic, and spectral properties of PN. Theoretical predictions often suffer from insufficient level of theory, incomplete basis set, or from neglecting several effects, for example, zero‐point vibrational correction (ZPVC). Therefore, we performed an extensive benchmark study on structural, electronic, and spectral properties of PN at the Hartree‐Fock, density functional theory (DFT), or even the coupled‐cluster levels. We paid special attention to the basis set effect. We tested three variants of Dunning's aug‐cc‐pVXZ basis sets with the size from double‐ζ to sextuple‐ζ, as well as Jensen's aug‐pc‐n, aug‐pcJ‐n, and aug‐pcSseg‐n basis sets, where n = 1‐4. Obtained energetics, PN distance, dipole moment, vibrational frequencies, and nuclear magnetic resonance (NMR) parameters were extrapolated to the complete basis set limit (CBS) using three‐ or two‐parameter formulas. The 31P NMR shieldings estimated with the aug‐cc‐pVXZ and aug‐cc‐pV(X + d)Z basis sets strongly depend on the basis set size providing scattered convergence patterns toward CBS. The Hartree‐Fock self‐consistent field (HF‐SCF) NMR parameters evinced similar behavior as the coupled‐cluster data. The only smooth convergence was achieved using the aug‐cc‐pCVXZ basis sets that include core‐valence effects. The KT3 functional underestimated the phosphorus CBS shieldings by about 12 ppm compared to coupled cluster with singles and doubles (CCSD) (T). Nevertheless, KT3 unambiguously surpasses the HF‐SCF and CCSD levels that provide 31P shieldings that are lower by about 150 ppm and 24 ppm compared to CCSD(T). The convergence of nitrogen shieldings was regular for all basis set hierarchies and all theoretical methods. Relativistic and vibrational effects on selected properties were also discussed.

The Effects of Split Valence Basis Sets on Muon Hyperfine Interaction in Guanine Nucleobase and Nucleotide Structures

The DFT cluster method was employed to investigate the electronic structures and muonium hyperfine interactions in guanine nucleobase and nucleotide using three different basis sets. The total energy and Fermi contact values were calculated for muon trapped at carbon '8'. The three basis sets, 6-31G, 6-311G and 6-311G(d,p), were used in tandem with the B3LYP functional. There are significant quantitative differences in the calculated total energy. 6-311G(d,p) produced the lowest total energy as compared to the other basis sets. The lowering of the total energy is due to the increase in the number of basis functions to describe the atomic orbitals, which is consistent with the postulate on basis set completeness. The 6-31G basis set produced the muon Fermi contact value that is the closest to the experimental value. The calculated Fermi contact values for the nucleobase and nucleotide are significantly lowered in going from the double-zeta to the triple-zeta basis set by 5% and 4% respectively. The lowering of the Fermi contact value can be attributed to the extension of the triple-zeta basis set in describing the valence atomic orbitals. The presence of the sugar phosphate group in the nucleotide instead of the methyl group tends to lower the Fermi contact value. Thus, the sugar phosphate group should be taken into consideration when designing a calculation model.

Performance of Delta-Coupled-Cluster Methods for Calculations of Core-Ionization Energies of First-Row Elements.

A thorough study of the performance of delta-coupled-cluster (ΔCC) methods for calculations of core-ionization energies for elements of the first long row of the periodic table is reported. Inspired by the core-valence separation (CVS) scheme in response theories, a simple CVS scheme of excluding the vacant core orbital from the CC treatment has been adopted to solve the convergence problem of the CC equations for core-ionized states. Dynamic correlation effects have been shown to make important contributions to the computed core-ionization energies, especially to chemical shifts of these quantities. The maximum absolute error (MaxAE) and standard deviation (SD) of delta-Hartree-Fock results for chemical shifts of core-ionization energies with respect to the corresponding experimental values amount to more than 1.7 and 0.6 eV, respectively. In contrast, the inclusion of electron correlation in ΔCC singles and doubles augmented with a noniterative triples correction [ΔCCSD(T)] method significantly reduces the corresponding deviations to around 0.3 and 0.1 eV. With the consideration of basis set effects and the corrections to the CVS approximation, ΔCCSD(T) has been shown to provide highly accurate results for absolute values of core-ionization energies, with a MaxAE of 0.22 eV and SD of 0.13 eV. To further demonstrate the usefulness of ΔCCSD(T), calculations of carbon K-edge ionization energies of ethyl trifluoroacetate, a molecule of significant interest to the study of X-ray spectroscopy and dynamics, are reported.

Antioxidative activity analyses of some pyridazine derivatives using computational methods

Pyridazine-derivative compounds have attracted considerable attention in different fields for many years due to their various biological activities such as antimicrobial and antitumoral. Simultaneously, antioxidative activity is one of the most important properties of them. With this perspective, antioxidative properties of eight different pyridazine derivatives have been investigated in accordance with three main mechanisms (HAT, SET, and SPLET). The investigation has been carried out with HF/6-31+G(d,p), B3LYP/6-31G(d,p), B3LYP/6-31+G(d,p), and MP2/6-31+G(d,p) level of theories in both gas and liquid phases. Furthermore, several molecular descriptors, bond and proton dissociation enthalpies, ionization potentials, proton affinities, and electron transfer enthalpies of investigated molecules have been calculated and antioxidative properties of the molecules have been sorted in accordance with the calculated values. Besides, effects of methods, basis sets, and solvent have been discussed. This computational study has determined the antioxidative capacity of 1A2D as the highest in each studied method and phases.

Static second-hyperpolarizability of diffuse electron cyclic compounds M2A2 (M = Be, Mg, Ca; A = Li, Na, K): Effect of basis set and electron correlation

In the present work, a number of cyclic planar molecules M2A2 (M = Be, Mg, Ca; A = Li, Na, K) are considered to calculate second-hyperpolarizability using HF, MP2, CCSD, CCSD(T) and DFT methods and 6-311++G(d,p), Sadlej-pVTZ, aug-pc-2 and aug-cc-pVTZ basis sets. The molecules are thermodynamically stable. The diffuse electrons on alkali metals are more efficient on enhancing the magnitude of second-hyperpolarizability. The two-state model can explain the origin of second-hyperpolarizability. The rather highest magnitude of second-hyperpolarizability (107 au) of the Ca2K2 complex arises from the intense lower energy transition. The vibrational contribution to second-hyperpolarizability has been found to be significant.

Vibrational analysis of the ubiquitous interstellar molecule cyclopropenylidene (c-C3H2): the importance of numerical stability

Recent work on cyclopropenylidene, c-CH, sought to improve on past ab initio results with a complete basis set (CBS) quartic force field method capable of predicting fundamental bands to within 5 cm−1 accuracy of gas-phase spectroscopy experiments for semirigid molecules. It was suggested that a problematic coupling between n-body correlation and 1-particle basis set effects prevented a proper application of this method for the out-of-plane bending vibrations of c-CH. We establish here that the actual source of this anomalous behaviour is numerical instability in the out-of-plane bending quartic force constants. It is found that the use of the normal equations to solve for the quartic force field, as well as a bending coordinate grid which is too compact, leads to errors of ca. 20 cm−1 in and . Our revised analysis shows and to be 980 cm−1 and 777 cm−1, respectively.

Basis Set Effects in the Description of the Cl-O Bond in ClO and XClO/ClOX Isomers (X = H, O, and Cl) Using DFT and CCSD(T) Methods

The performance of a group of density functional methods of progressive complexity for the description of the ClO bond in a series of chlorine oxides was investigated. The simplest ClO radical species and the two isomeric structures XClO/ClOX for each X = H, Cl, and O were studied using the PW91, TPSS, B3LYP, PBE0, M06, M06-2X, BMK, and B2PLYP functionals. Geometry optimizations and reaction enthalpies and enthalpies of formation for each species were calculated using Pople basis sets and the (aug)-cc-pVnZ Dunning sets, with n = D, T, Q, 5, and 6. For the calculation of enthalpies of formation, atomization and isodesmic reactions were employed. Both the precision of the methods with respect to the increase of the basis sets, as well as their accuracy, were gauged by comparing the results with the more accurate CCSD(T) calculations, performed using the same basis sets as for the DFT methods. The results obtained employing composite chemical methods (G4, CBS-QB3, and W1BD) were also used for the comparisons, as well as the experimental results when they are available. The results obtained show that error compensation is the key for successful description of molecular properties (geometries and energies) by carefully selecting the method and basis sets. In general, expansion of the one-electron basis set to the limit of completeness does not improve results at the DFT level, but just the opposite. The enthalpies of formation calculated at the CCSD(T)/aug-cc-pV6Z for the species considered are generally in agreement with experimental determinations and the most accurate theoretical values. Different sources of error in the calculations are discussed in detail.

A theoretical study on 1H/13C/31P NMR chemical shifts, and the correlation between 2JP–H and the electronic structure of different phosphoryl benzamide derivatives

A comprehensive study was performed on 1H/13C/31P NMR chemical shifts (CSs) of some phosphoryl benzamide derivatives (R1C6H5C(O)NHP(O)R2R3), [R1 = CH3, OCH3, NO2, F, Cl, Br and R1, R2 = NHC(CH3)3 or NC4H8O] by the GIAO method to find the most correlated level of theory with experimental values. All the structures (C1C12) were firstly optimized at B3LYP, BP86, PBE1PBE, M06-2X, MPWB1K and MP2 methods with 6–31 + G* basis set. Computed structural parameters demonstrate that BP86 has the best agreement to experimental values. The def2-TZVP and aug-cc-pVDZ basis sets were also employed to inspect the effect of different basis sets. The correlation between experimental and computational values prove that 6–31 + G* basis set is the optimum case regarding minimization of the costs and results. Chemical shifts were calculated at all mentioned combinations and compared with experimental data, which demonstrate that in accordance with structural parameters, BP86/6−31 + G* gives the best results. Calculating 2JPH values of studied compounds, focusing on the comparison between experimental and theoretical results was another aim of this study. Computed values of 2JPH at the optimum level of theory reveal an acceptable agreement with experimental data. Eventually, the dependency between 2JPH values and the bonding structures was inspected. NBO analysis at BP86/6−311++G** explicates the relationship between the electronic properties of studied compounds and 2JPH values.

Second hyperpolarizability of diffuse-electron compounds M-NH3, M-NLi3 and M-NLi3-M of alkaline earth metals: Effect of lithiation

Present investigation demonstrates that push electron effect of nitrogen in M … NH3is reduced rather than enhanced upon lithiation which has been explained by natural bond orbital analysis showing that nitrogen atom in NLi3 changes it's state of hybridization from sp3 to sp2 leaving the 2pz orbital partially occupied. This makes NLi3 a weak acceptor of electrons from alkaline earth metals. When the second alkaline earth metal is introduced the 2pz orbital of nitrogen attains the maximum occupation as a result of cumulative charge transfer from two metal atoms. However, the push electron effect still operates resulting in the diffuse electron localized over the metals. Large enhancement of second hyperpolarizability (106 au) in M … NLi3 has been rationalized by its low lying intense transitions. Effect of basis set on the second hyperpolarizability has been studied at the CCSD level which showed that Sadlej's pol and 6–311++G(3df,3pd) basis sets give comparable results that are obtained for the aug-cc-pVTZ basis set. The results of second hyperpolarizability calculated by using different DFT functionals are found to be consistent with the CCSD results obtained for the aug-cc-pVTZ basis set.

Aggregation of lactic acid in cold rare-gas matrices and the link to solution: a matrix isolation-vibrational circular dichroism study.

The matrix isolation (MI) technique has been utilized with vibrational circular dichroism (VCD) spectroscopy to obtain MI-VCD spectra of lactic acid (LA) in cold argon matrices, in addition to their MI-IR spectra. The experiments have been done at three different deposition temperatures (10 K, 16 K and 24 K) under different Ar flow rates so that different degrees of LA self-aggregation occur. The structural and spectral investigations of the LA monomer and the larger (LA)2,3,4 aggregates have been undertaken at three levels of theory (B3LYP/6-311++G(2d,p), B3LYP-D3BJ/6-311++G(2d,p) and B3LYP-D3BJ/def2-TZVPD) to evaluate the effects of dispersion correction and basis sets on optimized structures, relative conformer energies, and IR/VCD spectral features. Interestingly, the relative conformer energies vary considerably with and without dispersion correction, especially when the molecule gets larger and when it is placed in solution. Such uncertainties in the relative energies and in the vibrational band positions and IR/VCD intensities highlight the challenges in interpreting experimental spectroscopic data, especially those obtained in solution. With the narrow MI-IR band width and highly characteristic MI-VCD spectral features and the trend observed at three temperatures, we have been able to correlate the spectral features confidently to those of the LA monomer and the larger (LA)2,3,4 aggregates, with the aid of theoretical modeling. Finally, by noting the similarity of MI-IR and especially MI-VCD features obtained at 24 K with those of the 0.2 M solution, and with the aid of spectral simulation at the B3LYP-D3BJ/def2-TZVPD level, a composition of LA aggregates dominated by the LA tetramer and trimer has been identified. This conclusion differs from the previous reports where the LA dimer was identified as the main species at even higher concentration in CDCl3. The present work showcases the power of MI-VCD spectroscopy in aiding solution spectral assignment and in providing insight into the complex self-aggregation behavior of LA in solution.

Electron Propagator Methods for Vertical Electron Detachment Energies of Anions: Benchmarks and Case Studies.

Ab initio electron propagator methods are efficient and accurate means of calculating vertical electron detachment energies of closed-shell, molecular anions with nuclei from the first three periods. Basis set extrapolations enable definitive comparisons between electron propagator results and benchmarks defined by total energy differences obtained with coupled-cluster, single, double, plus perturbative triple substitution theory. The best compromises of accuracy and efficiency are provided by the renormalized, partial third-order, diagonal (P3+) self-energy and by the nondiagonal, renormalized, second-order (NR2) approximation. The outer-valence Green function, the two-particle-one-hole Tamm-Dancoff approximation, the third-order algebraic diagrammatic construction, and the renormalized third-order methods also are examined. A detailed analysis of errors for small anions is performed. Case studies include F-(H2O) and Cl-(H2O) complexes, C5H5-, two P2N3- pentagonal rings, and a superhalide, Al(BO2)4-, whose electron detachment energy is more than double those of the halide anions. These applications illustrate the versatility of electron propagator methods, their utility for interpreting negative-ion photoelectron spectra, and their promise in the discovery of unusual properties and patterns of chemical bonding. Composite methods, which combine basis set effects calculated at the relatively efficient diagonal, second-order level and higher correlation effects calculated with small basis sets, provide excellent estimates of basis set-extrapolated P3+ or NR2 results and facilitate applications to large molecules. In the P3+ and NR2 methods, a judicious choice of low-order couplings between hole operators that correspond to the assumptions of Koopmans's theorem and operators that describe final-state relaxation and polarization and initial-state correlation leads to predictive accuracy, computational efficiency, and interpretive lucidity.

Interaction-induced electric (hyper)polarizability in the dihydrogen-neon pair: basis set and electron correlation effects.

We investigated the interaction (hyper)polarizability of neon-dihydrogen pairs by performing high-level ab initio calculations with atom/molecule-specific, purpose-oriented Gaussian basis sets. We obtained interaction-induced electric properties at the SCF, MP2, and CCSD levels of theory. At the CCSD level, for the T-shaped configuration, around the respective potential minimum of 6.437 a0, the interaction-induced mean first hyperpolarizability varies for 5 < R/a0 < 10 as[Formula: see text]Again, at the CCSD level, but for the L-shaped configuration around the respective potential minimum of 6.572 a0, this property varies for 5 < R/a0 < 10 as[Formula: see text] Graphical Abstract Interaction-induced mean dipole polarizability ([Formula: see text]) for the T-shaped configuration of H2-Ne calculated at the SCF, MP2, and CCSD levels of theory.

Three Ligands with Biomedical Importance: Binding to Small ZnS Quantum Dots

We have performed the first systematic density functional theory study of the coordination of three biomedically significant ligands, acetylcysteine, dihydrolipoic acid, and dopamine, to a small quantum dot (QD), Zn6S6. An exhaustive search for the global minima structures of the ligands and of the ligand–QD species identified several isomers of each compound close in energy to the global minimum structures. The isomeric variety is explained by the presence of several functional groups in the ligands and thus by numerous possibilities of their coordination to the QD. The global minimum structures of the three ligand–QD complexes were further studied with a larger basis set and implicit water effects. The three complexes were shown to be stable, with the anionic ligand species coordinated to the QD being generally more stable than the neutral compounds. The QD distortions because of the coordination with the anionic ligands were much more pronounced than those with the neutral ligands. Charge transfer from both the neutral and anionic ligands to the QD upon the ligand coordination was detected.

Conformational and electronic properties of hydroquinone adsorption on C60 fullerenes: Doping atom, solvent and basis set effects

Hydroquinone (HQ) is widely used as a reducing agent with well-known antioxidant properties. The interaction with pristine and doped fullerenes seems to have a promising research field particularly for the drug delivery and sensor applications. In this research, sensitivity of silicon or boron doped and undoped fullerenes to the HQ molecule and adsorption energies of HQ interacted fullerene cages and dopant effect on the electronic properties were mainly examined with density functional theory (DFT).M06-2X and B3LYP functionals were used for the gas phase and water media. The effect on the basis sets for the investigated systems was also searched by using 6-31G(d) and ccpvdz basis sets.