Use Of Large Basis Sets Research Articles

V 51 solid-state NMR and density functional theory studies of vanadium environments in V(V)O2 dipicolinic acid complexes

(51)V solid-state NMR and density functional theory (DFT) investigations are reported for a series of pentacoordinate dioxovanadium(V)-dipicolinate [V(V)O(2)-dipicolinate] and heptacoordinate aquahydroxylamidooxovanadium(V)-dipicolinate [V(V)O-dipicolinate] complexes. These compounds are of interest because of their potency as phosphatase inhibitors as well as their insulin enhancing properties and potential for the treatment of diabetes. Experimental solid-state NMR results show that the electric field gradient tensors in the V(V)O(2)-dipicolinate derivatives are affected significantly by substitution on the dipicolinate ring and range from 5.8 to 8.3 MHz. The chemical shift anisotropies show less dramatic variations with respect to the ligand changes and range between -550 and -600 ppm. To gain insights on the origins of the NMR parameters, DFT calculations were conducted for an extensive series of the V(V)O(2)- and V(V)O-dipicolinate complexes. To assess the level of theory required for the accurate calculation of the (51)V NMR parameters, different functionals, basis sets, and structural models were explored in the DFT study. It is shown that the original x-ray crystallographic geometries, including all counterions and solvation water molecules within 5 A of the vanadium, lead to the most accurate results. The choice of the functional and the basis set at a high level of theory has a relatively minor impact on the outcome of the chemical shift anisotropy calculations; however, the use of large basis sets is necessary for accurate calculations of the quadrupole coupling constants for several compounds of the V(V)O(2) series. These studies demonstrate that even though the vanadium compounds under investigations exhibit distorted trigonal bipyramidal coordination geometry, they have a "perfect" trigonal bipyramidal electronic environment. This observation could potentially explain why vanadate and vanadium(V) adducts are often recognized as potent transition state analogs.

The magnetizability, rotational g tensor and quadrupole moment of the boron trihalides

We present the results of an ab initio study of the molecular Zeeman properties—that is, the magnetizabilities, rotational g tensors, and electric quadrupole moments—for BX3 (X = F, Cl, Br, I) within Hartree–Fock and density-functional theories. Basis-set convergence is ensured by the use of large basis sets of London atomic orbitals. Calculated trends are discussed and comparisons are made with available experimental data.

Coupled Cluster Theory and Multireference Configuration Interaction Study of FO, F2O, FO2, and FOOF

Structures, vibrational frequencies, atomization energies at 0 K, and heats of formation at 298 K were obtained for four oxyfluoride molecules, several of which are known to present difficulties for single reference ab initio methods. Whereas much of this work was carried out with coupled cluster theory, multireference configuration interaction calculations were also performed, as an independent check on the reliability of the former. The use of large basis sets (up through augmented sextuple zeta quality in some cases) and a simple basis set extrapolation formula enabled us to accurately estimate the complete basis set limit. However, to achieve near chemical accuracy (±1 kcal/mol) in the thermodynamic properties, it was necessary to include three corrections to the frozen core atomization energies, in addition to the zero-point vibrational energy: (1) a core/valence correction; (2) a Douglas−Kroll−Hess scalar relativistic correction; and (3) a first-order atomic spin−orbit correction. Several approache...

Conformations and energetics of sulfur and selenium diimides.

The geometries and energetics of different conformations of sulfur and selenium diimides E(NR)(2) (E = S, Se; R = H, Me, (t)Bu, C(6)H(3)Me(2)-2,6, SiMe(3)) have been studied by using various ab initio and DFT molecular orbital techniques. The syn,syn conformation is found to be most stable for parent E(NH)(2), but in general, the preferred molecular conformation for substituted chalcogen diimides is syn,anti. In the case of E(NH)(2) the present calculations further confirm that syn,syn and syn,anti conformations lie energetically close to each other. From the three different theoretical methods used, B3PW91/6-31G proved to be the most suitable method for predicting the geometries of chalcogen diimides. The optimized geometrical parameters are in a good agreement with all available experimental data. While qualitative energy ordering of the different conformations is independent of the level of theory, the quantitative energy differences are dependent on the method used. The performance and reliability of higher level ab initio calculations and DFT methods using large basis sets were tested and compared with experimental information where available. All of the higher level ab inito methods give very similar results, but the use of large basis sets with the B3PW91 method does not increase the reliability of the results. The combination of CCSD(T)/cc-pVDZ with the B3PW91/6-31G-optimized geometries is found to be the method of choice to study energetic properties of chalcogen diimides.

Transition states and energy barriers from density functional studies: Representative isomerization reactions

AbstractThree representative isomerization reactions (HNC → HCN, CH3NC → CH3CN, and N2H2 trans → cis and sin) have been studied using both the LCGTO–LSD and LCGTO–NLSD density functional methods and employing a new algorithm for the search and the refinement of the transition‐state structures. The inclusion of the nonlocal corrections and the use of large basis sets improve the reliability of the energetic parameters. Results are in good agreement with previous accurate first‐principle computations and available experimental data. © John Wiley & Sons, Inc.

Large-scale ab initio calculations for C3

Large-scale calculations by the single, double, and perturbative triple excitation coupled cluster [CCSD(T)] method have been carried out for C3. A linear equilibrium geometry with Re=1.2945 Å was obtained. The use of large basis sets and the inclusion of connected triple substitutions is crucial for an accurate representation of the extremely shallow bending potential. Rovibrational term energies were calculated from a three-dimensional CCSD(T) potential (basis: 177 contracted Gaussian-type orbitals) by the discrete variable representation (DVR). Compared with the best previous ab initio calculations [P. Jensen et al., J. Chem. Phys. 97, 3399 (1992)] agreement with experiment is improved by almost an order of magnitude. The errors in the wave numbers of the fundamentals are −7.7 (ν1), 0.9 (ν2), and 0.6 (ν3) cm−1, respectively.

Failure of net atomic charge models to represent the van der Waals envelope electric potential of n‐alkanes

AbstractTraditional net atomic charge models were found unsatisfactory for representing the molecular electric potential (MEP) of n‐alkanes ethane through decane in their van der Waals envelopes. The MEP of these molecules was calculated by ab initio methods. Mulliken atomic charges were erratic and gave root mean square (rms) relative errors of fit to the MEP ranging from 152 to 607% with the 6‐31 + + g** basis set. Fitting the MEP with potential‐derived net atomic charges (PD charges) gave errors ranging from 51 to 62% with the same basis set. The use of larger basis sets, inclusion of electron correlation, use of more MEP data points, or relaxation to optimal structural geometry did not improve significantly the representation of the MEP by net atomic charges. In many cases PD charges of hydrogen atoms were negative, and carbon atoms were positive. To improve the representation of the MEP of n‐alkanes, augmentation of the model with nonatomic sites was investigated with the program PDM93. Models with additional charge sites located between hydrogens, on a line bisecting the CH2 group, achieved fits to the MEP with errors reduced to 8% or less, except for n‐butane, where the fitting error was 16%. The PD models augmented with methylene bisector sites generally show positive hydrogen charges. They also show CH2 group charge alternation along the n‐alkane chains. The augmented charge models were consistent with the observed quadrupole moment of ethane and gave satisfactory predictions for the crystal structures of pentane and octane. © 1994 by John Wiley & Sons, Inc.

Accurate prediction of static dipole polarizabilities with moderately sized basis sets

The development is described of a basis set of moderate size optimized for the computation of the dipole polarizability of reasonably large molecules consisting of hydrogen and p-block elements up to iodine. The mean polarizability, polarizability anisotropy and dipole moment for hydrides of the first four rows of the periodic table, obtained at both the SCF and MP2 levels, are compared with those obtained using the previously developed 6–31 G(+ sd + sp) basis set, as well as larger basis sets, and with experiment. For the series of diatomic halogens, X2, and the halomethanes, CH3X (X = F, C1, Br, I), electric properties are obtained in excellent agreement with those resulting from use of larger basis sets, and also with experiment.

Theoretical characterization of the reaction NH2+NO→products

The potential energy surface for NH2+NO has been characterized using complete active space self-consistent-field (CASSCF)/derivative calculations to determine the stationary point geometries and frequencies followed by internally contracted configuration interaction (ICCI) calculations to determine the energetics. Production of N2+H2O is found to involve a complex mechanism. The initially formed NH2NO undergoes a 1,3-hydrogen shift to give an HNNOH isomer (with the substituents trans about the NN bond and cis about the NO bond) which undergoes subsequent cis–trans isomerizations about the NN and NO bonds before decomposing to N2+H2O. The saddle point for production of N2+H2O has an approximately rectangular arrangement of one H atom, the two N atoms, and the O atom. This process does not involve a barrier with respect to NH2+NO. Formation of HN2+OH can occur from any of the isomers of HNNOH with no barrier, but the overall process is endothermic by 0.7 kcal/mol [based on the computed Δ Hf0 (0 K) of HN2]. The results obtained in this work are qualitatively the same as previous work, but both the stationary point geometries and energies should be more reliable due to the use of larger basis sets and more extensive inclusion of electron correlation effects.

THEORETICAL PREDICTIONS OF THE STRUCTURE AND VIBRATIONAL INFRARED FREQUENCIES OF 2,2′-DICHLORODIETHYL SULFIDE AND HYDROLYSIS PRODUCTS

Abstract We report the computed equilibrium geometries and vibrational infrared frequencies for 2,2′-dichlorodiethyl sulfide and six related hydrolysis products, utilizing the HF/6-311G** and MP2/6-31G* levels of theory. A comparison of the calculated frequencies to the corresponding experimental data yields correction factors for the vibrational modes. In general, we find the use of larger basis sets tends to improve the consistency of the correction factors while inclusion of electron correlation tends to improve their accuracy. The agreement between the experimental and calculated data enables us to make predictions about the major features of the infrared spectra of the hydrolysis species for which no infrared data have been reported.

Quantum Monte Carlo for the Electronic Structure of Atoms and Molecules

Since the late 1960s molecular orbital (MO) theory has dominated the development of ab initio quantum chemistry. Specifically, the Hartree­ Fock-Roothaan (HFR) (1-3) formalism of the self-consistent field (SCF) method, which was greatly facilitated by the development of gaussian basis sets as suggested by Boys (4, 5), and the post-Hartree-Fock methods of configuration interaction (CI) (6-8), multiconfiguration SCF (MCSCF) (9, 10), many-body perturbation theory (MBPT) and coupled-cluster methods (CCM) (11), and Moller-Plesset perturbation theory (MPPT) (12). With the advent of high speed vector supercomputers the field has virtually exploded; larger molecules or very high accuracy for small molecules are now possible. In addition to such capability has come more accurate knowledge of the size of I-particle and N-particle basis sets required for high accuracy (13-16). Not only does the use of large basis sets require large memory and file-storage capability, but HFR and post-HFR algorithms contain significant bottlenecks to vectorization and parallelization. Although many new and efficient matrix methods have been developed

Mechanism of keto Å enol tautomerism of ionized vinyl alcohol versus acetaldehyde and their dissociation to C 2H 3O + and H ·. An ab initio molecular orbital study

In complete accord with experiment, ab initio molecular orbital calculations provide a detailed description of the potential energy surface for some isomers of the C 2H 4O +· ions. In particular, it is predicted that the ionized hydroxy(methyl)carbene, H 3CCOH +·, is a stable C 2H 4O +· isomer and serves as the key intermediate in the isomerization/dissociation processes of the cation radical of gaseous vinyl alcohol. A comparison between the results of semi-empiric (MINDO/3 and MNDO) and ab initio calculations at various levels of theory suggests that (i) MINDO/3 fails to describe properly the central features of the C 2H 4O +· energy surface, (ii) MNDO gives results which are qualitatively similar to those obtained by the more elaborate ab initio procedures and (iii) inclusion of the effects of correlation and zero-point energies, as well as the use of large basis sets, are essential for obtaining a reliable insight into the gas phase chemistry of these and related cation radicals.

Finite perturbation MCSCF and CI calculations of nuclear spin-spin coupling constants for some molecules with multiple bonds

Non-empirical finite perturbation calculations at the Hartree-Fock, multiconfigurational self-consistent field and configuration interaction levels of approximation are presented for the Fermi contact contribution in multiply-bonded molecules ethene, formimide, formaldehyde, ethyne and hydrogen cyanide. The finite perturbation-multiconfigurational SCF (FPMC) method (with few configurations) is free from the UHF triplet instabilities normally present in single configuration coupled Hartree-Fock (CHF) calculations of the Fermi contact (and spin-dipolar) contribution for π-bonded systems. The behaviour of coupling constants, calculated using FPMC for multiply-bonded systems parallels the behaviour of the CHF coupling constants in comparable systems with single bonds only. The effects of dynamic electron correlations are important and are obtained using the Cl method. After accounting for the orbital contribution by means of the single configuration CHF method, agreement with experiment is excellent for systems containing only carbon and hydrogen, when a double-zeta quality basis set is used. For systems containing nitrogen and oxygen agreement is still reasonable, but the use of larger basis sets seems to be necessary if good agreement with experiment is to be obtained.

Metal ion influence on hydrogen bonds in solvent and ligands

The application of quantum chemical calculations of the all-electron ab initio type studies of metal influence on neighbouring hydrogen bonds has been extended successively to new and larger model compounds during the past decade. Starting with comparatively small systems accessible to fair methodical accuracy due to the use of larger basis sets, some principal effects have been revealed, such as bond contraction, net bond stabilization, charge transfer effects and the increase of rotational barriers around the hydrogen bond [1, 2]. At the same time, such investigations have proved once more the need for the use of ab initio type calculations and the incapability of semiempirical procedures for the treatment of metal-solvent or metal-ligand interactions. The consideration of slightly larger systems such as e.g. ion/water/formamide [3] has shown that the effect of the metal ion extends over a long series of bonds, which implies a need for comparatively large ‘subunits’ of the molecules (or rather ‘supermolecular’) system for a conclusive quantum theoretical study. This fact was also revealed by the quantum chemically predicted electronic rearrangements taking place in complexes with more than one ligand with the ability to form chelate structures [4]. For this reason, the applicability of minimal basis sets, allowing an extension of the supermolecular model system to considerably larger subunits, had to be tested. The conclusions of such test [2, 3] have shown that such basis sets can be used for the evaluation of intermolecular geometrical parameters and relative energy effects, still maintaining sufficient accuracy, especially if basis set error corrections like the counterpoise procedure [5] are employed. The data of ab initio calculations for ion/ligand interaction form the basis of three main approaches to more complex systems: 1. The evaluation of pair and three-body potentials representing the basis for the construction of interaction potentials used in methods like Monte Carlo of Molecular Dynamics calculations on large ensembles of ions and molecules and/or macromolecules [ e.g. 6–8]. 2. The ‘static’ treatment of large supermolecular species with small basis sets for the evaluation of geometries, binding energies, electron density distribution and other data for solvated ions or ion/ligand complex. 3. The possibility of the construction of supermolecular electrostatic perturbation fields representing the influence of molecules at larger distances from the ion and/or directly involved ligand [9,10]. Among these methods, numbers 2 and 3 are especially suitable to reveal some effects of the metal ions on surrounding solvent and other ligand molecules. For the demonstration of the use of small basis sets in combination with electrostatic potentials, solvation of ions in water and some nonaqueous solvents are mentioned [9, 10]. The treatment of crystal growth also seems to be a promising field of application for this approach [11]. The application of calculations of the type 2 mentioned above for the study of metal ion influence on hydrogen bonds in base pairs of nucleic acids [12–14] seems to be another useful example of the capability of theoretical approaches in the field of bioinorganic chemistry. These examples also demonstrate, however, the importance of basis set error corrections and hence a careful methodical control in the course of such investigations. An example of cooperative experimental and quantum chemical research can be given in the field of ion/peptide interactions, where experimental data for biological protein/metal complexes are compared with metal complexes of small peptides, which on the other hand are accessible again to ab initio calculations with minimal basis set.

ChemInform Abstract: SEMIEMPIRICAL NDDO CALCULATIONS WITH STO‐3G AND 4‐31G BASIS SETS

Possible refinements of semiempirical methods include the use of larger basis sets and of correlated wave functions. These possibilities are investigated in semiempirical NDDO SCF calculations with the STO-3G and 4-31G basis sets, and in correlated calculations at the STO-3G level. The present approach is characterized by the analytical evaluation of all one-center terms and two-electron integrals, and the semiempirical adjustment of the remaining one-electron integrals and the nuclear repulsions. The NDDO SCF results tend to reproduce the correspondingab initio results more closely than experimental data, even if they are parametrized with respect to experiment. The explicit inclusion of electron correlation at the STO-3G level improves the calculated results only slightly.

Semiempirical NDDO calculations with STO-3G and 4-31G basis sets

Possible refinements of semiempirical methods include the use of larger basis sets and of correlated wave functions. These possibilities are investigated in semiempirical NDDO SCF calculations with the STO-3G and 4-31G basis sets, and in correlated calculations at the STO-3G level. The present approach is characterized by the analytical evaluation of all one-center terms and two-electron integrals, and the semiempirical adjustment of the remaining one-electron integrals and the nuclear repulsions. The NDDO SCF results tend to reproduce the correspondingab initio results more closely than experimental data, even if they are parametrized with respect to experiment. The explicit inclusion of electron correlation at the STO-3G level improves the calculated results only slightly.

A systematic theoretical study of harmonic vibrational frequencies: The ammonium ion NH4+ and other simple molecules

Analytic gradient techniques have been used to predict the harmonic vibrational frequencies of HCN, H2CO, H2O, CH4 and NH4+ at several levels of molecular electronic structure theory. Basis sets of double zeta, double zeta plus polarization, and extended plus polarization quality have been used in conjunction with self-consistent-field and configuration interaction methods. For the four spectroscopically characterized molecules, comparison with theory is particularly appropriate because experimental harmonic frequencies are available. For the 16 vibrational frequencies thus considered, the DZ SCF level of theory yields average errors of 166 cm−1 or 8.0%. The DZ+P SCF results are of comparable accuracy, differing on the average from experiment by 176 cm−1 or 8.3%. With the extended basis set, the comparable SCF frequency errors are only slightly less. The explicit incorporation of correlation effects qualitatively improves the agreement between theoretical and experimental harmonic vibrational frequencies. The DZ CI frequencies differ on the average by only 44 cm−1 or 2.0%. Perhaps surprisingly, the use of larger basis sets in conjunction with CI including all singly and doubly excited configurations leads to larger average errors in the vibrational frequencies. For example, the DZ+P CI frequencies have average errors of 80 cm−1 or 3.5%. Thus it seems clear that higher excitations (probably unlinked clusters especially) have a significant effect (order of 50 cm−1) on the theoretical prediction of polyatomic vibrational frequencies. The apparent discrepancy between the theoretical and experimental equilibrium geometry of CH4 is resolved here, and shown to have been a simple consequence of basis set incompleteness. Finally, the gas phase NH4+ equilibrium bond distance is predicted to be 1.022 Å, or 0.01–0.02 Å shorter than found by Ibers and Stevenson for NH4+ in crystalline NH4Cl and NH4F.

Finite-field method calculations of molecular polarisabilities. I. Theoretical basis and limitations of SCF and Galerkin treatments

In calculation of polarisabilities by the finite-field method, a number of problems arise which require critical examination. In this paper some of the most important of these are considered for calculations at the SCF level and illustrated by results obtained for the polarisabilities of LiH, Li 2 and N 2. The special basis-set requirements for obtaining accurate molecular polarisabilities are discussed. The problem of achieving basis-set convergence is also considered. An approximation at the SCF level — the weak formulation or Galerkin method — is introduced to reduce the computational expense resulting from the use of large basis sets. It is found that this method gives results comparable with those of the full SCF treatment with considerable savings of time. Correlation effects will be discussed in part II.