Addition Of Diffuse Functions Research Articles

Corrigendum: Homochiral [2.2]Paracyclophane Self-Assembly Promoted by Transannular Hydrogen Bonding.

In Figure 1 of this Communication, the units on the vertical axis of the top right plot were incorrectly given as δ instead of Δδ. The corrected plot is given below. […] Top right: nonlinear curve fitting of concentration-dependent NH chemical shift data (CDCl3) fit to an isodesmic model. Additionally, the Communication incorrectly identifies the level of theory used as M06-2X/6-31+G*. The correct level of theory is M06-2X/6-31G* (without the addition of diffuse functions). The authors apologize for these oversights.

All-electron segmented contraction basis sets of triple zeta valence quality for the fifth-row elements

All-electron contracted Gaussian basis set of triple zeta valence quality plus polarisation functions (TZP) for the elements Cs, Ba, La, and from Hf to Rn is presented. Douglas–Kroll–Hess (DKH) basis set for fifth-row elements is also reported. We have recontracted the original TZP basis set, i.e., the values of the contraction coefficients are re-optimised using the second-order DKH Hamiltonian. By addition of diffuse functions (s, p, d, f, and g symmetries), which are optimised for the anion ground states, an augmented TZP basis set is constructed. Using the B3LYP hybrid functional, the performance of the TZP–DKH basis set is assessed for predicting atomic ionisation energy as well as spectroscopy constants of some compounds. Despite its compact size, this set demonstrates consistent, efficient, and reliable performance and will be especially useful in calculations of molecular properties that require explicit treatment of the core electrons.

Augmented Gaussian basis sets for the elements K, Sc–Kr, Rb, and Y–Xe: Application in HF, MP2, and DFT calculations of molecular electric properties

Augmented Gaussian basis sets of triple and quadruple zeta valence qualities plus polarization functions for the atoms K, from Sc to Kr, Rb, and from Y to Xe are presented. They were constructed from the all-electron unaugmented sets by addition of diffuse functions (s, p, d, f, g, and h symmetries) that were optimized for the anion ground states. From these sets, Hartree–Fock, second-order Mϕller–Plesset perturbation theory, and density functional theory electric dipole moment and polarizabilities for a sample of molecules as well as for Cun and Agn (n⩽4) clusters were calculated and compared with theoretical and experimental values available in the literature.

Negative Electron Affinities from DFT: Fluorination of Ethylene

Four simple density functional theory methods are investigated to assess how well they can describe subtle variations in negative vertical electron affinities arising due to the successive fluorination of ethylene, where the magnitude of the variations is well below the absolute accuracy of the methods. Three of the approaches (two based on Koopmans' theorem and one using a potential wall) are able to describe the trends in the affinities using both compact and very diffuse basis sets. The best results are obtained using the potential wall. The fourth approach uses a conventional energy difference evaluation, which is only applicable when the basis set is compact; the breakdown upon addition of diffuse functions is strikingly illustrated. The results are interpreted in terms of the apatial extent of the relevant orbitals and the signs and values of the orbital energies. The study highlights the potential predictive value of simple DFT methods for describing trends in negative affinities.

Augmented Gaussian basis set of double zeta valence quality for the atoms Rb and Y–Xe: Application in DFT calculations of molecular electric properties

Augmented Gaussian basis set of double zeta valence quality plus polarization functions for the atoms Rb and from Y to Xe is presented. It was generated from the all-electron unaugmented set by addition of diffuse functions (s, p, d, and f symmetries) that were optimized for the anion ground states. From this set, density functional theory electric dipole moment and dipole polarizability for a sample of molecules were calculated and compared with theoretical and experimental values available in the literature. Our results give good agreement with experimental and benchmark values.

Augmented Gaussian basis sets of double and triple zeta valence qualities for the atoms K and Sc–Kr: Applications in HF, MP2, and DFT calculations of molecular electric properties

Augmented Gaussian basis sets of double and triple zeta valence qualities plus polarization functions for the atoms K and from Sc to Kr are presented. They were generated from the all-electron unaugmented sets by addition of diffuse functions (s, p, d, f, and g symmetries) that were optimized for the anion ground states. From these sets, Hartree–Fock, second-order Møller–Plesset perturbation theory, and density functional theory electric dipole moment and dipole polarizability calculations for a sample of molecules were carried out. Comparison with theoretical and experimental values available in the literature was done.

Absence of Conjugation in Vibrational Spectra and Assignments of Dichloro(vinyl)phosphine and Dichloro(phenyl)phosphine Oxides and Sulfides

The structure and conformational stability of dichloro(vinyl)phosphine and dichloro(phenyl)- phosphine oxides and sulfides were investigated using calculations at the DFT/6-311G** and ab initio ones at the MP2/6-311G** level. We know from our previous results that the addition of diffuse functions to a valence triple zeta basis with polarization functions might lead to an unbalanced basis, which performs even worse than the smaller basis without diffuse functions, as it is the case for the 6-311++G** basis set in the Gaussian program. For large energy differences between conformers, DFT works very well, in some cases even better than MP3 or MP4. The vinyl derivatives were predicted to exist in a cis/gauche conformational equilibrium with cis (the PX bond, X being oxygen or sulfur eclipses the vinyl groups) being the predominant conformer at ambient temperature. In the phenyl case case the two planar forms are equivalent minima. The asymmetric potential function for the internal rotation was determined for each of the molecules. The vibrational frequencies were computed and the spectra, where possible, were compared with the experimental ones. Normal coordinate calculations were carried out and potential energy distributions were calculated for the molecules in the cis and gauche conformations (in the vinyl case, planar one for phenyl), providing a complete assignment of the vibrational lines to symmetry coordinates in the molecules. From our results and their analysis we conclude, in agreement with literature results based on localized orbitals, that conjugation effects are absent - or at least negligible - as compared with electrostatic ones in determining the structures of the stable conformers in both the vinyl and the phenyl derivatives. The P-O bond should be a highly polarized triple bond, as confirmed by analysis of Mulliken populations. The polarization turned out to be much less in the sufides due to the much smaller electronegativity of sulfur as compared with oxygen.

The equilibrium OH bond length

The equilibrium structure of 36 small molecules containing OH bonds, including molecules with an internal hydrogen bond, is reviewed from the literature. The structures are redetermined or determined, if necessary, using high level ab initio calculations at the CCSD(T) level of theory with basis sets of quintuple zeta quality and with a correction for the core correlation. The possibility of calculating accurate ab initio OH bond lengths at different levels of theory (MP2/VTZ, MP2/VQZ, CCSD(T)/VTZ, and CCSD(T)/AVTZ) is examined. All methods agree provided a small offset correction is taken into account. In most cases, the addition of diffuse functions does not improve the results. The MP2 method appears to be satisfactory whenever the non-dynamical electron correlation is small, which is the most typical situation. The various results are merged to demonstrate the following quantitative correlation between r e(OH) and ‘isolated’ OH stretching frequencies, relevant for predictive use: r e(OH) [Å] = 1.2261(76)–7.29(21) × 10−5 νis(OH) [cm−1].

Current–voltage curves for molecular junctions computed using all-electron basis sets

We present current–voltage ( I– V) curves computed using all-electron basis sets on the conducting molecule. The all-electron results are very similar to previous results obtained using effective core potentials (ECP). A hybrid integration scheme is used that keeps the all-electron calculations cost competitive with respect to the ECP calculations. By neglecting the coupling of states to the contacts below a fixed energy cutoff, the density matrix for the core electrons can be evaluated analytically. The full density matrix is formed by adding this core contribution to the valence part that is evaluated numerically. Expanding the definition of the core in the all-electron calculations significantly reduces the computational effort and, up to biases of about 2 V, the results are very similar to those obtained using more rigorous approaches. The convergence of the I– V curves and transmission coefficients with respect to basis set is discussed. The addition of diffuse functions is critical in approaching basis set completeness.

A theoretical study of neutral and reduced tetracyano- p-quinodimethane (TCNQ)

The molecular structure of neutral, anionic, and dianionic tetracyano- p-quinodimethane (TCNQ), as well as the electron affinity of TCNQ, have been studied with HF, MP2, and different density functional theory (DFT) procedures. The optimized geometries compare well with the available experimental data, although the C N bond distance is not correctly described at the MP2 level. The calculated parameters are rather insensitive to the basis set employed, and the addition of diffuse functions does not yield significant changes. When the extra electrons are added, the central ring of TCNQ progressively becomes more aromatic. Compared with the CCSD(T) estimate, the value of the adiabatic electron affinity is overestimated at the DFT level. The B3P86 functional leads to the largest deviations, higher than 1 eV, whereas the BLYP functional affords the best results. At the MP2 level, the value obtained after projection of the major spin contaminating component (PMP2) is in good agreement with the CCSD(T) result. Single-point PMP2 calculations over DFT-optimized geometries are suggested as a low-cost alternative strategy to study more extended systems.

Polarization consistent basis sets. III. The importance of diffuse functions

A sequence of diffuse functions to be used in connections with the previously defined polarization consistent basis sets are proposed based on energetic criteria and results for molecular properties. At the Hartree–Fock level the addition of a single set of diffuse s- and p-functions significantly improves the convergence of calculated electron affinities. A corresponding analysis at the density functional level indicates that only systems with high electron affinities have well-defined basis set limits with common exchange-correlation functionals that have electron self-interaction errors. The majority of reported density functional calculations of electron affinities appear to be artifacts of the limited basis set used. The good agreement with experiments for such calculations is most likely due to a reasonable modeling of the physics of the anionic species, rather than being a theoretically sound procedure. For molecular properties like dipole and quadrupole moments, and static polarizabilities, the addition of diffuse functions up to d-functions is required to reach the basis set limit in a consistent fashion, but higher order angular momentum functions are significantly less important.

DFT Calculations for Cu-, Ag-, and Au-Containing Molecules

The physicochemical properties of a set of molecules containing Cu, Ag, or Au atoms were calculated using the GAUSSIAN program suite, with the purpose of investigating the various density functional theory (DFT) approaches for subsequent application in cluster calculations. The test set comprised the copper-based molecules CuH, CuO, CuS, Cu2, CuCl2-, CuCH3, CuC2H2, Cu2(HCO2)4(H2O)2, and Cu6H6(PH3)6 and the silver and gold diatomics AgH, AgO, AgS, Ag2, AgCu, AuH, AuO, AuS, Au2, AuCu, and AuAg. The DFT methods used were SVWN, BLYP, and BPW91, together with the DFT hybrids B3LYP and B3PW91. The calculations were carried out with the basis sets LANL2MB, LANL2DZ, 3-21G, and 6-311G (when available). The properties calculated were the molecular geometry, vibrational frequencies, and dissociation energies. It was found that all the DFT-based methods, particularly when allied with the LANL2DZ basis set, produced results which are significantly closer to experimental values than those of the traditional Moller−Plesset (MP2) electron correlation method and which are also applicable to considerably larger molecules. Over the whole test set of molecules, the RMS errors of the four “BX” methods, in conjunction with LANL2DZ, were typically 3−4% for geometries, 6−8% for frequencies, and 10−16% for dissociation energies, with BPW91 and the popular B3LYP at the lower and upper ends of these ranges, respectively, and with the errors being overestimates and underestimates, respectively. The corresponding values for SVWN and MP2 were 2% and 6%, 12% and 12%, and 33% and 42%, with these errors typically being ± and +, + and −, and + and −, with + and − representing overestimates and underestimates, respectively. While the best bond lengths are produced by SVWN (a local spin density approximation), which is not uncommmon, this advantage over the gradient corrected (BX) methods is only slight, and the latter are markedly superior for frequencies and especially dissociation energies. Not supported by the present results are the notions that (all) pure DFT methods underestimate metal−ligand bond lengths and overestimate bond strengths and that hybrid methods are superior (and neither that DFT methods are overcorrelated). Testing on a subset of molecules with BPW91/LANL2DZ revealed no benefit in supplementing this basis set by the addition of diffuse functions, nor of the counterpoise correction. There appear to be specific incompatibilities with some method/basis set combinations, and even the continuing availability of 3-21G for these metals is questionable. Because of its accuracy and reliability, the combination BPW91/LANL2DZ is recommended for these noble-metal systems (and to extensions such as the cluster-model approach to adsorption of a molecule on a metal surface).

Ab initio computation of the UV resonance Raman intensity pattern of aqueous imidazole

AbstractThe UV resonance Raman (RR) spectrum of aqueous imidazole was modeled by evaluating the gradients of the resonant π→π* excited state, using various levels of theory. To take account of H‐bonding effects, two water molecules were included in the model, one accepting an H‐bond from and the other donating an H‐bond to imidazole. The ground‐state geometry and force field of the ImH·2H2O complex was computed via SQM‐DFT theory, with the B3LYP functional, yielding good agreement with experimental vibrational wavenumbers for the in‐plane imidazole modes. Evaluation of excited‐state gradients with the semiempirical ZINDO method, which has previously been applied successfully to metalloporphyrin RR spectra, failed to reproduce the imidazole UVRR spectrum. However, the ab initio CIS method gave fairly good results. Agreement with the experimental intensity pattern improved when minimal STO‐3G or 3–21G* basis sets were upgraded to 6–31G*, but further refinement, to 6–31G**, did not alter the pattern, and addition of diffuse functions actually degraded the spectral quality. Likewise, more elaborate levels of ab initio theory, TDDFT and CASSCF(4,4), gave poorer agreement with experiment then CIS. Thus optimum modeling of the UVRR spectrum was achieved with the popular CIS/6–31G* methodology. Application of the Kramers–Kronig transform frequency correction to the ωk2 approximation (‘short‐time limit’) altered the intensity distribution only slightly. Copyright © 2001 John Wiley & Sons, Ltd.

Should the standard basis sets be augmented with diffuse functions on hydrogens to provide a reasonable description of the lowest Rydberg state of hydrogen-containing molecules?

Augmentation of the standard basis sets with the diffuse functions, which were optimized for non-Rydberg anions on the heavy atoms only, may not be adequate for calculating Rydberg states of molecules. Addition of diffuse functions on the hydrogens to such a basis set used for calculations of Rydberg states of hydrogen-containing species can make up for this deficiency and lead to a reasonable description. This gives the possibility of using the standard basis sets (e.g., the 6-31G(d,p) and 6-311G(d,p) basis sets) augmented by diffuse functions, both on the heavy atoms and on the hydrogen atoms, for these calculations and, therefore, provides an alternative to optimizing diffuse functions specifically to describe Rydberg orbitals. Inclusion of diffuse s functions on hydrogens is less important in calculations of non-Rydberg hydrogen-containing anions.

Structures and relative stabilities of bisulfite ion isomers

The structure and equilibria of the bisulfite ion in the gas phase are investigated using ab initio electronic structure methodology. The structures analysed were the C 3v structure and the syn and anti tautomers of the C s structure. Optimized geometries and total energies were determined for a variety of basis sets and levels of theory. Polarization functions had profound effects on both geometries and relative energies. Addition of diffuse functions was found to affect significantly both relative stabilities and geometries at the MP2/3–21 + G ∗ level. However, diffuse functions had minor effects at the MP2/6–31 + G ∗ level. Inclusion of electron correlation via second-order (MP2) and full fourth-order (MP4SDTQ) Møller-Plesset perturbation treatments was found to have moderate effects on geometries and relative stabilities. Normal mode vibrational frequencies were calculated for all isomers studied. The lowest energy structure was found to be an asymmetric form of the syn conformation of the C s tautomer.

A b i n i t i o determination of the nonlinear optical properties of HCl

A b initio calculations of the static- and frequency-dependent dipole polarizability α and first and second hyperpolarizabilities β and γ of HCl are presented. Static polarizabilities are determined using the self-consistent field (SCF), second-order Mo/ller–Plesset perturbation theory (MP2), the coupled-cluster single and double excitation method (CCSD), and CCSD with a perturbative estimate of triple excitations [CCSD(T)]. The effect of basis set expansion, particularly the addition of diffuse functions up to g type, is explored. It is found that for highly accurate calculations, f functions are necessary on Cl, but g functions have a much smaller effect. The frequency-dependent hyperpolarizabilities for wavelengths of 694.3 and 1319 nm are determined at the SCF and MP2 levels of theory. The CCSD(T) static values, scaled using MP2 dispersion, are found to be in good agreement with experiment. Electron correlation is found to play a significant role in both the static and dynamic quantities. Use of the SCF dispersion as a percentage correction to the static MP2 hyperpolarizability, however, is found to be a good approximation to the total MP2 frequency-dependent hyperpolarizability at the frequencies studied. The effects of vibrational contributions to the polarizabilities are discussed.

Ab initio scf studies on thioformic acid: basis-set effects

Ab initio calculations on monothioformic acid (HCOSH, TFA) were performed using the restricted Hartree-Fock formalism and 13 standard Gaussian basis sets in order to determine the basis-set dependence of the geometries, energy barriers and vibrational spectra of cis- and trans-TFA. Trans-TFA was found to be the more stable with the trans-cis energy difference varying between 5.0 and 13.8 kJ mol −1and the trans-cis energy barrier height ranging from 31.2 to 42.1 kJ mol −1. The inclusion of polarization functions in the basis set unproved considerably the calculated values compared with the available experimental data. Furthermore, the addition of diffuse functions did not noticeably influence the results. A normal-coordinate analysis based on HF/6–311G ∗∗ calculated Cartesian force field was performed to describe the assignment of the fundamental vibrational frequencies.

An ab initio molecular orbital study of the structures and energies of neutral and charged bimolecular complexes of NH3 with the hydrides AHn (A = N, O, F, P, S, and Cl)

AbstractHartree‐Fock 6‐31G(d) structures for the neutral, positive ion, and negative ion bimolecular complexes of NH3 with the first‐ and second‐row hydrides AHn (AHn = NH3, OH2, FH, PH3, SH2, and ClH) have been determined. All of the stable neutral complexes except (NH3)2, the positive ion complexes with NH3 as the proton acceptor, and the negative ion complexes containing first‐row anions exhibit conventional hydrogen bonded structures with essentially linear hydrogen bonds and directed lone pairs of electrons. The positive ion complex NH4+ …︁ OH2 has the dipole moment vector of H2O instead of a lone pair directed along the intermolecular line, while the complexes of NH4+ with SH2, FH, and ClH have structures intermediate between the lone‐pair directed and dipole directed forms. The negative ion complexes containing second‐row anions have nonlinear hydrogen bonds. The addition of diffuse functions on nonhydrogen atoms to the valence double‐split plus polarization 6‐31G(d,p) basis set usually decreases the computed stabilization energies of these complexes. Splitting d polarization functions usually destabilizes these complexes, whereas splitting p polarization functions either has no effect or leads to stabilization. The overall effect of augmenting the 6‐31G(d,p) basis set with diffuse functions on nonhydrogen atoms and two sets of polarization functions is to lower computed stabilization energies. Electron correlation stabilizes all of these complexes. The second‐order Møller–Plesset correlation term is the largest term and always has a stabilizing effect, whereas the third and fourth‐order terms are smaller and often of opposite sign. The recommended level of theory for computing the stabilization energies of these complexes is MP2/6‐31+G(2d,2p), although MP2/6‐31+G(d,p) is appropriate for the negative ion complexes.

Basis set and correlation effects on computed positive ion hydrogen bond energies of the complexes AHn · AHn + 1+1: AHn = NH3, OH2, and FH

AbstractBasis set expansion and correlation effects on computed hydrogen bond energies of the positive ion complexes AHn · AHn + 1+1, for AHn = NH3, OH2 and FH, have been evaluated. The addition of diffuse functions on nonhydrogen atoms is the single most important enhancement of split‐valence plus polarization basis sets for computing hydrogen bond energies. Basis set enhancement effects appear to be additive in these systems. The correlation energy contribution to the stabilization energies of these complexes is significant, with the second order term being the largest term and having a stabilizing effect. The third order term is smaller and of opposite sign, while the fourth order term is smaller yet and stabilizing. As a result, computed MP4 stabilization energies are bracketed by the MP2 and MP3 energies. The overall effect of basis set enhancement is to decrease hydrogen bond energies, whereas the addition of electron correlation increases stabilization energies.

Basis set and correlation effects on computed negative ion hydrogen bond energies of the complexes AHn � AHn?1?1: AHn ? NH3, OH2, and FH

Basis set and correlation effects on computed hydrogen bond energies of the negative ion complexes AHn · AHn−1−1, for AHn NH3, OH2, and FH, have been evaluated. The addition of diffuse functions on nonhydrogen atoms to valence double- and triple-split plus polarization basis sets [6-31G(d, p) and 6-311G(d, p)] significantly decreases binding energies by 9–19 kcal/mol, depending on the particular complex and the level of theory. Adding diffuse functions to hydrogens has a negligible effect, while replacing the single set of polarization functions on each atom by two sets alters energies by 1 kcal/mol or less. Electron correlation increases the hydrogen bond energies of these complexes and has a greater effect for basis sets without diffuse functions. Since the Hartee-Fock energies computed with these basis sets are already too large, correlation energy calculations should not be performed in these cases. For basis sets including diffuse functions, the correlation energy contribution to the binding energies of these complexes is significant, with the Moller-Plesset second-order term being the largest term and having a stabilizing effect of from 3–6 kcal/mol. The third and fourth order terms are smaller, and may be of opposite sign. As a result, the MP2 and MP4 energies differ by no more than 1 kcal/mol, with the MP2 stabilization energy being greater except for N2H5−1. The computed standard solvation enthalpy of OH−1 by H2O based on either MP4/6–311 + G(2d, 2p) or MP2/6–31 + G(d, p) electronic energies is –26.8 kcal/mol, in excellent agreement with a recent gas-phase experimental measurement.