Basis set effects on calculated geometries: 6-311++G** vs. aug-cc-pVDZ

The effect of basis sets on MP2 and CCSD calculated geometries has been investigated for a series of small organic molecules with two to four nonhydrogen atoms. Whereas 6-311++G** usually leads to satisfactory structures, this was not true with aug-cc-pVDZ, although it uses more basis functions than the former set. In addition, the smaller 6-311++G** invariably leads to lower calculated energies than aug-cc-pVDZ. With a given basis set, CCSD gives more satisfactory calculated geometries than MP2, but with a much greater computation time. For the compounds in this report, B3LYP/6-311++G** is quite effective in giving satisfactory calculated geometries at a relatively small computational cost.     

Convergence of third order correlation energy in atoms and molecules

We have investigated the convergence of third order correlation energy within the hierarchies of correlation consistent basis sets for helium, neon, and water, and for three stationary points of hydrogen peroxide. This analysis confirms that singlet pair energies converge much slower than triplet pair energies. In addition, singlet pair energies with (aug)-cc-pVDZ and (aug)-cc-pVTZ basis sets do not follow a converging trend and energies with three basis sets larger than aug-cc-pVTZ are generally required for reliable extrapolations of third order correlation energies, making so the explicitly correlated R12 calculations preferable.     

The role of the basis set and the level of quantum mechanical theory in the prediction of the structure and reactivity of cisplatin

In this article, we conducted an extensive ab initio study on the importance of the level of theory and the basis set for theoretical predictions of the structure and reactivity of cisplatin [cis‐diamminedichloroplatinum(II) (cDDP)]. Initially, the role of the basis set for the Pt atom was assessed using 24 different basis sets, including three all‐electron basis sets (ABS). In addition, a modified all‐electron double zeta polarized basis set (mDZP) was proposed by adding a set of diffuse d functions onto the existing DZP basis set. The energy barrier and the rate constant for the first chloride/water exchange ligand process, namely, the aquation reaction, were taken as benchmarks for which reliable experimental data are available. At the B3LYP/mDZP/6‐31+G(d) level (the first basis set is for Pt and the last set is for all of the light atoms), the energy barrier was 22.8 kcal mol^?1, which is in agreement with the average experimental value, 22.9 ± 0.4 kcal mol^?1. For the other accessible ABS (DZP and ADZP), the corresponding values were 15.4 and 24.5 kcal mol^?1, respectively. The ADZP and mDZP are notably similar, raising the importance of diffuse d functions for the prediction of the kinetic properties of cDDP. In this article, we also analyze the ligand basis set and the level of theory effects by considering 36 basis sets at distinct levels of theory, namely, Hartree‐Fock, MP2, and several DFT functionals. From a survey of the data, we recommend the mPW1PW91/mDZP/6‐31+G(d) or B3PW91/mDZP/6‐31+G(d) levels to describe the structure and reactivity of cDDP and its small derivatives. Conversely, for large molecules containing a cisplatin motif (for example, the cDDP‐DNA complex), the lower levels B3LYP/LANL2DZ/6‐31+G(d) and B3LYP/SBKJC‐VDZ/6‐31+G(d) are suggested. At these levels of theory, the predicted energy barrier was 26.0 and 25.9 kcal mol^?1, respectively, which is only 13% higher than the actual value. © 2012 Wiley Periodicals, Inc.     

Localization function study of excitation processes in a set of small isoelectronic molecules

Electron localization function (ELF) theory is used to characterize changes that occur upon excitation from ground singlet to first excited triplet states in a series of isoelectronic 16‐electron molecules including H₂CCH₂, HNCH₂, H₂CO, HNNH, HNO, and O₂ (ground triplet to excited singlet). ELF allows one to visualize lone pair or nonbonding electrons, and in these cases the π→π* or n→π excitation processes involved lead to an effective 90° rotation of the electronic structure about one heavy atom center and consequent distortion towards pyramidal symmetry about both heavy atom centers. The heavy atom bond lengths change very little in those cases where effectively two‐center three‐electron bonds can be formed (HNNH, HNO, and O₂) while a significant lengthening occurs in those cases where hydrogen atoms prevent such interactions (H₂CCH₂, HNCH₂, and H₂CO). It is shown that both ELF basin populations and atoms‐in‐molecules (AIM) delocalization indices reflect expected bond orders for conventional single and double bonds provided one compares the ratio of the molecular quantities rather than their absolute magnitudes. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1702–1711, 2001     

Toward universal substituent constants: Model chemistry sensitivity of descriptors from the quantum theory of atoms in molecules

The quantum theory of atoms in molecules (QTAIM) provides a theoretical foundation to determine the properties of functional groups through additive atomic contributions. Many studies have used QTAIM in their analyses with a variety of electronic structure methods, but it is unknown if the properties measured using one model chemistry, the combination of the electronic structure method and basis set, can be compared to those measured by another. Here, we evaluate the sensitivity of QTAIM functional group and bond critical point properties using six functionals and seven basis sets. High-level B2PLYPD3-BJ/aug-cc-pV5Z reference values are provided for 116 functional groups and the property sensitivity with respect to these values are evaluated based on absolute deviations and by assessing linear relationships. Functional group properties, including charges, dipoles, quadrupoles and volumes, were found to be mostly insensitive to choice of computational model chemistry. However, due to structural and topological inconsistencies, the 6-31G(d) basis set is not recommended for use. Bond critical point properties varied with choice of model chemistry, but models incorporating hybrid functionals and triple-ζ basis sets provided values suitable for use in regression studies.     

Computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules

In the presence of a static, nonhomogeneous magnetic field, represented by the axial vector at the origin of the coordinate system and by the polar vector , assumed to be spatially uniform, the chiral molecules investigated in this paper carry an orbital electronic anapole, described by the polar vector . The electronic interaction energy of these molecules in nonordered media is a cross term, coupling and via , one third of the trace of the anapole magnetizability a_αβ tensor, that is, . Both and W^BC have opposite sign in the two enantiomeric forms, a fact quite remarkable from the conceptual point of view. The magnitude of predicted in the present computational investigation for five chiral molecules is very small and significantly biased by electron correlation contributions, estimated at the density functional level via three different functionals. © 2016 Wiley Periodicals, Inc.     

Constitutive modeling of radiation effects on the permanent set in a silicone elastomer

When a networked polymeric composite under high stress is subjected to irradiation, the resulting chemical changes like chain scissioning and crosslink formation can lead to permanent set and altered elastic modulus. Using a commercial silicone elastomer as a specific example we show that a simple 2-stage Tobolsky model in conjunction with Fricker's stress transfer function can quantitatively reproduce all experimental data as a function of radiation dosage and the static strain at which radiation is turned on, including permanent set, stress-strain response, and net crosslink density.     

On the basis‐set dependence of local and integrated electron density properties: Application of a new computer program for quantum‐chemical density analysis

A new computer program for post‐processing analysis of quantum‐chemical electron densities is described. The code can work with Slater‐ and Gaussian‐type basis functions of arbitrary angular momentum. It has been applied to explore the basis‐set dependence of the electron density and its Laplacian in terms of local and integrated topological properties. Our analysis, including Gaussian/Slater basis sets up to sextuple/quadruple‐zeta order, shows that these properties considerably depend on the choice of type and number of primitives utilized in the wavefunction expansion. Basis sets with high angular momentum (l = 5 or l = 6) are necessary to achieve convergence for local properties of the density and the Laplacian. In agreement with previous studies, atomic charges defined within Bader's Quantum Theory of Atoms in Molecules appear to be much more basis‐set dependent than the Hirshfeld's stockholder charges. The former ones converge only at the quadruple‐zeta/higher level with Gaussian/Slater functions. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Contracted well-tempered Gaussian basis sets in SCF calculations on the ground and excited electronic states of neutral and ionized diatomic molecules containing first-row atoms

Summary Calculations were done on ground and excited states of C₂, C ₂ ⁺ , C ₂ ^– , N₂, N ₂ ⁺ , O₂, O ₂ ⁺ , O ₂ ^– , CO, CO⁺, CO²⁺, and CO^– using contracted well-tempered basis sets. The (14s 10p) basis sets were augmented with threed, one or twof, and oneg functions. Total energies, orbital energies, and spectroscopic constants were compared with the best available computational data.     

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.     

A critical study of basis set effects and the use of approximate natural orbitals in SCF-CI calculations of molecular geometries and heats of reaction

SCF-CI calculations have been performed on a number of chemical reactions between closed shell molecules in order to determine the heats of reaction. Contracted Gaussian type atomic basis sets of three different qualities were used and the CI calculations were performed in a truncated approximate natural orbital space. The conclusions to be drawn from these calculations are rather pessimistic. For heats of reaction, errors up to 6 kcal/mole are obtained on the SCF-level with a double zeta plus polarization atomic basis. A further improvement is only possible if extended basis sets are used. Correlation effects on heats of reaction are of the same size and CI calculations are therefore only meaningful with large atomic basis sets.For the CI calculations a one-electron space of approximate natural orbitals, obtained from second order RS perturbation theory, was used. Different truncations, using the occupation number as criterion, were tested. The general conclusion is that errors in energy differences obtained with a truncated basis set are of the same magnitude as the error in the total correlation energy. In practice this means that not more than 20–30% of the approximate natural orbitals can be deleted if the error is to be kept less than a few kcal/mole.Finally the truncation error in calculations of bond distances was tested for a few cases. Errors of around 10% of the total change due to correlation were found when 30% of the lowest occupied natural orbitals were deleted.     

The performance of the new 6-31G(##) basis set: molecular structures and vibrational frequencies of transition metal carbonyls

The performance of the newly proposed 6-31G(##) basis set for calculating the equilibrium structure and vibrational frequencies of transition metal carbonyl complexes has been studied at the HF and DFT levels of theory. The 6-31G(##) basis set has been constructed by augmentation of the 6-31G basis set by diffuse and polarization functions, which are generated from the corresponding 6-31G basis AOs response functions obtained in the frame of propagator approach. The predicted values of bond distances and vibrational frequencies for the title compounds are in good agreement with the experimental data. The relative energies and HOMO-LUMO gaps were also estimated for the series of MCO complexes.     

A polarization propagator analysis of the geminal 31P-31P coupling in bis(difluorophosphino)amine⋆

Inner projections of the polarization propagator (IPPP) are used to decompose in through-space and through-bond contributions the two-bond P-P coupling in PF₂-NH-PF₂. This study is carried out using a ground state INDO wavefunction. Results for a phosphorus sp and spd atomic basis sets are compared. Several experimental trends are correctly reproduced using either of them. It is concluded that the overlap of the lone pair of both P atoms constitutes a very efficient pathway for transmitting through-space the spin information associated to the Fermi contact term.Part of a PhD thesis (H.O.G.) to be presented to the University of Buenos AiresFellow of the Argentine National Research Council (CONICET)Member of the Argentine National Research Council (CONICET)     

Structures of silylenoids and effects of metallic and haloid atoms on their stability

The structural characteristics of silylenoids, H2SiMX, where M = Li or Na and X = F or Cl, have been studied by ab initio calculations. H2SiMX can be represented as adducts of silylene H2Si with alkali metal halogenides, MX. The associative energies at different calculational levels of various structures of H2SiMX are given. Effects of metallic and haloid atoms on the stability of various structures of H2SiMX are also discussed in this paper.     

The RTAM electronic bibliography,version 17.0, on relativistic theory of atoms and molecules

The RTAM bibliography is freely available at rtam.csc.fi and the Version 17.0 of August 22, 2013 now contains 16,566 items from the year 1916–2013. “Production works” were systematically covered until 1999. Since the year 2000, mainly methodological papers were included. The methods and principles behind RTAM are described. © 2013 Wiley Periodicals, Inc.     

Development and testing of a compact basis set for use in effective core potential calculations on rhodium complexes

We present a set of effective core potential (ECP) basis sets for rhodium atoms which are of reasonable size for use in electronic structure calculations. In these ECP basis sets, the Los Alamos ECP is used to simulate the effect of the core electrons while an optimized set of Gaussian functions, which includes polarization and diffuse functions, is used to describe the valence electrons. These basis sets were optimized to reproduce the ionization energy and electron affinity of atomic rhodium. They were also tested by computing the electronic ground state geometry and harmonic frequencies of [Rh(CO)₂μ‐Cl]₂, Rh(CO)₂ClPy, and RhCO (neutral and its positive, and negative ions) as well as the enthalpy of the reaction of [Rh(CO)₂μ‐Cl]₂ with pyridine (Py) to give Rh(CO)₂ClPy, at different levels of theory. Good agreement with experimental values was obtained. Although the number of basis functions used in our ECP basis sets is smaller than those of other ECP basis sets of comparable quality, we show that the newly developed ECP basis sets provide the flexibility and precision required to reproduce a wide range of chemical and physical properties of rhodium compounds. Therefore, we recommend the use of these compact yet accurate ECP basis sets for electronic structure calculations on molecules involving rhodium atoms. © 2012 Wiley Periodicals, Inc.     

Pure through‐bond state in organic molecules for analysis of the relationship between intramolecular interactions and total energy

Ab initio configuration interaction through‐space/bond interaction analysis was proposed for the examination of specific intramolecular interactions including the effect of electron correlations. To test the effectiveness of our method, we applied it to rotational barrier in ethane. The results of our test suggest that the insensitivity of the ethane barrier to geometric relaxations is intimately connected with the cancellation of interactions through orbital overlaps and other factors. The orbital overlaps include exchange repulsion and hyperconjugation; other factors include classic Coulomb interaction and changes in bond orbital energy. The rotational state without the barrier (pure through‐bond state) can be achieved by deleting not only the “vicinal” interactions between the C? H bonds that belong to different methyl groups but also the “geminal” interactions within the methyl groups. Our mixing analysis of molecular orbitals supports the superiority of the staggered conformer by hyperconjugation. Moreover, it was demonstrated that our treatment could be applied to excited states as well as to the ground state, including electron correlation effects. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

The performance of the rapid estimation of basis set error and correlation energy from partial charges method on new molecules of the G3/99 test set

Experimental enthalpies of formation have been approximated using single-point Hartree–Fock (HF)–self-consistent-field (SCF) total energies plus the rapid estimation of basis set error and correlation energy from partial charges (REBECEP) energy corrections. The energy corrections are calculated from the HF–SCF partial atomic charges and optimized atomic energy parameters. The performance of the method was tested on 51 closed-shell neutral molecules (50 molecules from the G3/99 thermochemistry database plus urea, composed of H, C, N, O, and F atoms). The predictive force of the method is demonstrated, because these larger molecules were not used for the optimization of the atomic parameters. We used the earlier RECEP-3 [HF/6-311+G(2d,p)] and REBECEP [HF/6-31G(d)] atomic parameter sets obtained from the G2/97 thermochemistry database (containing small molecules) together with natural population analysis and Mulliken partial charges. The best results were obtained using the natural population analysis charges, although the Mulliken charges also provide useful results. The root-mean-square deviations from the experimental enthalpies of formation for the selected 51 molecules are 1.15, 3.96, and 2.92 kcal/mol for Gaussian-3, B3LYP/6-11+G(3df,2p), and REBECEP (natural population analysis) enthalpies of formation, respectively (the corresponding average absolute deviations are 0.94, 7.09, and 2.27 kcal/mol, respectively). The REBECEP method performs considerably better for the 51 test molecules with a moderate 6-31G(d) basis set than the B3LYP method with a large 6-311+G(3df,2p) basis set. Received: 10 March 2001 / Accepted: 5 July 2001 / Published online: 11 October 2001