Geometry optimization in ab initio SCF calculations. VII. Proton affinities and ion structures calculated with floating orbital geometry optimization (FOGO)

The FOGO method is used to calculate absolute proton affinities of the molecules H₂, HF, NH₃, H₂O, CH₃OH, C₂H₅OH, H₂O₂, CH₂O, CO, and CH₂CO. Comparison with experimental values demonstrates that the geometrical and energetical data resulting from this type of ab initio calculation are of chemical accuracy. Predictive data for higher energy isomers, such as hydroxymethylene and ethynol are given as possible aid for the identification of these species.     

Proton and lithium cation affinities calculated with floating orbital geometry optimization (FOGO)

The FOGO method is used to calculate proton affinities and lithium cation affinities. The molecules of primary interest in this study are the methyl-substituted amines. In addition, the lithium cation affinity of HF, H₂O, CH₃OH, H₂CO, and HCN are calculated for comparison. Geometries of all species are fully optimized with a double-zeta (DZ) basis set, including polarization on hydrogen and the first-row elements by floating orbitals. Comparison with experimental values demonstrates that structural data and proton affinities resulting from this type of ab initio calculation are of chemical accuracy. The lithium cation affinities are also reasonably well reproduced, but the small experimental differences are not within the accuracy, which can be expected from this type of calculation.     

Uniform quality gaussian basis sets for molecular calculations,I. C1 hydrocarbons

The optimality of MO basis sets of Gaussian functions, when constructed from AO basis sets optimized for the neutral atom or for atom ions, is investigated. A formal charge parameter Q is defined and used to adjust the AO basis sets to the molecular environment, by virtue of a simple quadratic expression. Calculations on a series of C₁ hydrocarbons (CH₂, CH₃, CH₃⁺, CH₃^?, CH₄) using 3G basis sets indicate considerable variations in the optimum Q value with the molecular species. The proposed method offers a simple alternative technique to a full molecular basis set optimization.     

Geometry optimization calculations in molecules containing second row atoms with various polarization function basis sets

Ab initio MO geometry optimization studies on a number of molecules containing second-row atoms using various polarization basis sets are presented. In particular the use of gaussian bond functions is shown to be a good substitute for the more conventional (and expensive) atom-centered d functions. Molecules examined to a double zeta plus polarization basis set level are HCP, P₂, SO, SO₂, H₂S, SF₂, CIF, HCl and Cl₂.     

NLO‐X (X = I–III): New Gaussian basis sets for prediction of linear and nonlinear electric properties

New adjusted Gaussian basis sets are proposed for first and second rows elements (H, B, C, N, O, F, Si, P, S, and Cl) with the purpose of calculating linear and mainly nonlinear optical (L–NLO) properties for molecules. These basis sets are new generation of Thakkar‐DZ basis sets, which were recontracted and augmented with diffuse and polarization extrabasis functions. Atomic energy and polarizability were used as reference data for fitting the basis sets, which were further applied for prediction of L–NLO properties of diatomic, H₂, N₂, F₂, Cl₂, BH, BF, BCl, HF, HCl, CO, CS, SiO, PN, and polyatomic, CH₄, SiH₄, H₂O, H₂S, NH₃, PH₃, OCS, NNO, and HCN molecules. The results are satisfactory for all electric properties tested; dipole moment (µ), polarizability (α), and first hyperpolarizability (β), with an affordable computational cost. Three new basis sets are presented and called as NLO‐I (ADZP), NLO‐II (DZP), and NLO‐III (VDZP). The NLO‐III is the best choice to predict L–NLO properties of large molecular systems, because it presents a balance between computational cost and accuracy. The average errors for β at B3LYP/NLO‐III level were of 8% for diatomic molecules and 14% for polyatomic molecules that are within the experimental uncertainty. © 2014 Wiley Periodicals, Inc.     

Applications of the model potential method to transition metal compounds

Model potential parameters and basis sets, presented previously for the transition metal atoms Sc through Hg, are tested in calculations of the transition metal compounds (CuF, CuCl, Cu₂, TiCl₄, ZrCl₄, CoF₆^3?, CoF₆^2?, AgH, AuH, CrF₆, ScO, ZrO, Cr₂, Mo₂). Calculated values of the bond distances, vibrational frequencies, and some transition energies (for Cu₂ and CoF₆^2?) are compared with those given by all-electron calculations with basis sets of high quality. Singlet-triplet splittings in Cu₂ and correlation energies in CrF₆^n? (n = 0, 1, and 2) are also examined. The satisfactory results obtained by these calculations strongly support the contention that the model potential method is a reliable and economical alternative to the ab initio Hartree-Fock-Roothaan method.     

K-shell ionization energies in molecules by SCF GF calculations

Energies of CH₄, NH₃, H₂O and C₂H₄ K-ionized molecules are calculated by means of a Group Function method using minimal or near minimal basis sets of STO's. Further results from very large basis sets are reported for CH₄, NH₃, and H₂O. Results seemingly do not suffer the shortcomings of a previous SCF MO treatment.     

The minimal basis set MINI-1—powerful tool for calculating intermolecular interactions. II. Ionic complexes

Optimum geometries and stabilization energies are determined for complexes of H₂O, NH₃, CH₄, C₂H₄, CO, and N₂ with metal cations including Li⁺, Na⁺, K⁺, Rb⁺, Be²⁺, Mg²⁺, Ca²⁺, Zn²⁺, and Al³⁺, for the complex (HO)₂PO ₂ ^– ...Mg²⁺ and for the complexes of water with F^–, Cl^–, and Br^– by SCF calculations employing the MINI-1 minimal gaussian basis sets. The Boys-Bernardi method was used to evaluate the superposition error. Comparison with the extended basis set results revealed that the MINI-1 set gives uniformly good results for a broad variety of ionic complexes and therefore should be preferred to other small basis sets.     

Correlation balance in basis sets for electronic structure calculations

The balanced addition of polarization functions to the 6–31G and 6–311G basis sets for correlated wave functions is evaluated using bond energy predictions at the MP 2 and full MP 4 levels as a measure of correlation-balanced basis sets. The homolytic dissociations of the XH bonds in H₂, CH₄, NH₃, H₂O, and HF and the XY bonds in C₂H₆, NH₂NH₂, HOOH, and CH₃OH are used as the basis for the evaluation. It is found that correlation balance is achieved for HH, XH, and XY bonds, particularly at the MP 2 level, only if at least as many polarization sets, and sometimes more, are added to the hydrogens as are added to the heavy atoms.     

Geometry optimization inab initio SCF calculations

The floating orbital geometry optimization (FOGO) described previously [1, 2] for atoms without polarized inner-shell electrons, is extended to the general case. Instead of the Hellmann-Feynman force a special gradient is calculated analytically and utilized in a variable metric procedure simultaneously with the ordinary energy gradient. Test calculations on a sample of 12 molecules were performed to check the efficiency of the method. The geometries obtained are better than those obtained with the corresponding double-zeta basis set. The most striking results, however, are excellent dipole moments.     

Ab initio calculations of isotropic hyperfine coupling constants in β-ketoenolyl radicals

Ab initio unrestricted Hartree–Fock (UHF ), unrestricted second-order Møller–Plesset (UMP 2) perturbation, unrestricted coupled cluster (UCCD ), and unrestricted quadratic configuration interaction (UQCISD ) calculations have been performed on the organic radicals CH₃, CH₃CH₂, CH₂CHCH₂, CH₃CHCOO^?, HCOCHCOH, CH₃COCHCOH, CH₃COCHCOCH₃, and CH₃COC(CH₃)COCH₃, using double-zeta and split-valence-plus-polarization basis sets. These radicals are derived from common organic ligands and have been observed in recent experimental work on tris(β-ketoenolato)cobalt(III) complexes. Their geometry has been optimized at the UHF level using the two mentioned basis sets. From these calcuations, values for the isotropic hyperfine coupling constants at the hydrogen atoms are predicted and compared with the experimental results. The usefulness of semiempirical extrapolations based on limited basis sets and treatment of electron correlation effects is carefully analyzed in the examples considered. © 1994 John Wiley & Sons, Inc.     

The use of biorthogonal sets in valence bond calculations

The “non-orthogonality problem” in valence bond theory is avoided by using two sets of basis functions, with a biorthogonality property, together with the method of moments. The basis set limit is reached whenall structures are included, but even truncated sets give good (though not monotonic) convergence. Calculations are reported for H₂, LiH, and H₂O.     

PCM study of the solvent and substituent effects on bond dissociation energies of the C?NO bond

Quantum chemical calculations are used to estimate the equilibrium C? NO bond dissociation energies (BDEs) for eight X? NO molecule (X = CCl₃, C₆F₅, CH₃, CH₃CH₂, iC₃H₇, tC₄H₉, CH₂CHCH₂, and C₆H₅CH₂). These compounds are studied by employing the hybrid density functional theory (B3LYP, B3PW91, B3P86) methods together with 6‐31G** and 6‐311G** basis sets and the complete basis set (CBS‐QB3) method. The obtained results are compared with the available experimental results. It is demonstrated that B3P86/6‐31G** and CBS‐QB3 methods are accurate for computing the reliable BDEs for the X? NO molecule. Considering the inevitably computational cost of CBS‐QB3 method and the reliability of the B3P86 calculations, B3P86 method with 6‐31G** basis set may be more suitable to calculate the BDEs of the C? NO bond. The solvent effects on the BDEs of the C? NO bond are analyzed and it is shown that the C? NO BDEs in a vacuum computed by using B3PW91/6‐311G** method are the closest to the computed values in acetontrile and the average solvent effect is 1.48 kcal/mol. Subsequently, the substituent effects of the BDEs of the C? NO bond are further analyzed and it is found that electron denoting group stabilizes the radical and as a result BDE decreases; whereas electron withdrawing group stabilizes the group state of the molecule and thus increases the BDE from the parent molecule. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Calculations of the Bond Dissociation Energies for NO<Subscript>2</Subscript> Scission in Some Nitro Compounds

The X(C,N,O)—NO₂ bond dissociation energy (BDE) for CH₃NO₂, C₂H₃NO₂, C₂H₅NO₂, HONO₂, CH₃ONO₂, C₂H₅ONO₂, NH₂NO₂, (CH₃)₂NNO₂ are computed using the DFT (B3LYP, B3PW91), the single and double-coupled cluster excited (CCSD), and the complete basis set (CBS-Q) methods, with the 6-311G^** and cc-pVDZ basis sets. By comparing the computed energies and experimental results, we find that the DFT method can not give good results of BDE, but, the BDEs generated by the CCSD/cc-pVDZ, CBS-Q are in good agreement with experimental values.     

Substituent effects in second-row molecules: Basis set performance in calculations of normal valency phosphorus and sulfur compounds

Ab inito molecular orbital calculations of the phosphorus- and sulfur-containing series PH₂X, PH₃X⁺, SHX, and SH₂X⁺ (X = H, CH₃, NH₂, OH, F) have been carried out over a range of Gaussian basis sets and the results (optimized geometrical structures, relative energies, and electron distributions) critically compared. As in first-row molecules there are large discrepancies between substituent interaction energies at different basis set levels, particularly in electron-rich molecules; use of basis sets lower than the supplemented 6-31G basis incurs the risk of obtaining substituent stabilizations with large errors, including the wrong sign. Only a small part of the discrepancies is accounted for by structural differences between the optimized geometries. Supplementation of low level basis sets by d functions frequently leads to exaggerated stabilization energies for π-donor substituents. Poor performance also results from the use of split valence basis sets in which the valence shell electron density is too heavily concentrated in diffuse component of the valence shell functions, again likely to occur in electron-rich molecules. Isodesmic reaction energies are much less sensitive to basis set variation, but d function supplementation is necessary to achieve reliable results, suggesting a marginal valence role for d functions, not merely polarization of the bonding density. Optimized molecular geometries are relatively insensitive to basis set and electron population analysis data, for better-than-minimal bases, are uniform to an unexpected degree.     

A theoretical study of the Si-O bond in disiloxane and related molecules

Summary A comparison of semi-empirical (MNDO) and ab initio (GAUSSIAN) calculations for disiloxane and related molecules is given. The STO-3G^* basis set well reproduced the observed geometries of disiloxane (*), DZP, TZVP) gave much poorer agreement with the observed geometries.Comparison of the STO-3G^* and the STO-3G basis sets demonstrates the necessity of including d-orbitals on the silicon. However, the semi-empirical MNDO program gave, despite the absence of d-orbitals, a better approximation to the molecular geometry than the complex ab initio basis sets.Force field parameters have been calculated for k_SiOSi, k_OSiO, 0.089 and 0.73 mdyneÅ/rad², and the SiOSiO torsion which has a V₁ potential of –0.68 kcal/mol. In addition, the HSiOH torsion is shown to have a three-fold potential of 0.78 kcal/mol. These are profoundly different from the analogous carbon-oxygen force constants, demonstrating that C-O parameters cannot be transferred to the corresponding Si-O systems.     

Minimal basis sets in calculations of intermolecular interaction energies

Several minimal (7, 3/3) Gaussian basis sets have been used to calculate the energies and some other properties of CH₄ and H₂O. Improved basis sets developed for these molecules have been extended to NH₃ and HF and employed to H₂CO and CH₃OH. Interaction energies between XH_n molecules have been calculated using the old and the new minimal basis sets. The results obtained with the new basis sets are comparable in accuracy to those calculated with significantly more extended basis sets involving polarization functions. Binding energies calculated using the counterpoise method are not much different for the new and the old minimal basis sets, and are likely to be more accurate than the results of much more extended calculations.     

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.