Sp Basis Set Research Articles

On the hybridization problem in H 2O by Hückel transformation theory

An orthogonal transformation of the oxygen valence AOs belonging to A 1 symmetry to an ω-hybridized sp basis set allows for useful simplifications reducing Hückel transformed matrix for ground state H 2O to nearly block-diagonal form. Neglecting delocalization of the hybrid lone pair into the bond, minimization of the resulting Hückel energy shows that for ω ≠ 0 the interbond angle opens beyond 90°. A further orthogonal transformation involving the B 2 y AO yields three orthogonal sp 2 hybrids of C 2v symmetry on oxygen which can be engaged in two equivalent straight O–H bonds making the experimental interbond angle and locally minimizing the Hückel energy of the valence electron configuration.

Electronic Spectrum and Photodissociation of ClONO in Comparison to BrONO

A theoretical study of the low-lying singlet and triplet states of ClONO is presented. Calculations of excitation energies and oscillator strengths are reported using multireference configuration interaction, MRD-CI, methods with the cc-pVDZ + sp basis set. The calculations predict the dominant transition, 4(1)A' <-- 1(1)A', at 5.70 eV. The transition 2(1)A' <-- 1(1)A', at 4.44 eV, with much lower intensity nicely matches the experimental absorption maximum observed around 290 nm (4.27 eV). The potential energy curves for both states are found to be highly repulsive along the Cl-O coordinate implying that direct and fast dissociation to the Cl + NO2 products will occur. Photodissociation along the N-O coordinate is less likely because of barriers on the order of 0.3 eV for low-lying excited states. A comparison between the calculated electronic energies related to the two dominant excited states of ClONO and BrONO indicates that the transitions lie about 0.6 eV higher if bromine is replaced by chlorine. The stratospheric chemistry implications of ClONO and BrONO are discussed.

Low-lying excited states and photodissociation studies of cis-BrONO

A computational study of the low-lying singlet and triplet states of bromine nitrite, cis-BrONO, is presented. Calculations of excitation energies and oscillator strengths are reported using multi-reference configuration interaction, MRD-CI, methods in conjunction with the cc-pVDZ + sp and cc-pVTZ + sp basis sets. In agreement with recent experimental work the calculations find two important transitions, namely to the states 21 A′ at 3.99 eV and 41 A′ at 5.27 eV. The corresponding measurements obtained 3.87 and 5.44 eV, respectively. Both states show multi-reference character, representing a linear combination of 3a″ → 4a″ and 9a′ → 10a′ transitions. The potential energy curves for the Br+ONO dissociation are repulsive for both states indicating possible photodissociation. BrO+NO products are not favoured because the corresponding potential energy curves show barriers on the order of 0.5 eV.

Ab Initio MRD-CI Study of the Electronic Spectrum of BrNO2 and Photofragmentation

Multi reference configuration interaction, MRD-CI, methods with the cc-pVDZ+sp and cc-pVTZ+sp basis sets were employed to determine the low-lying singlet and triplet electronic states of nitryl bromide, BrNO 2 . The calculations predict two very strong transitions, 3 1 A 1 ← X 1 A 1 and 3 1 B 2 ← X 1 A 1 , at 6.15 and 7.27 eV, respectively. At wavelengths that are atmospherically relevant to the BrNO 2 photolysis, 1 1 B 2 and 1 1 B 1 singlet states with vertical transition energies of 3.43 and 3.85 eV, respectively, are computed. The corresponding triplet states are lower in energy by 0.27 and 0.36 eV, respectively. Both singlet and triplet states are found to be highly repulsive along the Br-N coordinate and they dissociate to the ground-state fragments Br and NO 2 . The comparison between the first singlet excited state of BrNO 2 and ClNO 2 demonstrates that the transition is red-shifted by 80 nm from ClNO 2 upon replacement of chlorine by bromine. Furthermore, the most intense transition 3 1 A 1 ← X 1 A 1 of BrNO 2 has a 0.9 eV lower energy than that of ClNO 2 . These energy differences can be explained by the large halogen character of the orbitals involved in the electron excitations.

Excess Electron Attachment to Disulfide-Bridged l,l-Cystine. An ab Initio Study

The possibility of excess electron binding to cystine (consisting of two l-cysteine molecules linked via a disulfide bridge) in the gas-phase was studied at the second-order Moller−Plesset perturbation theory (MP2) level using the 6-31+G**+6(sp) basis sets. Several geometrically stable conformers and tautomers were found on the potential energy surfaces (PES) of both the neutral and anionic species. The most stable neutral isomer has proven to (i) involve two canonical rather than zwitterionic cysteine monomers, (ii) possess no inter-monomer hydrogen bonds, and (iii) exhibit an extended structure due to the presence of four intra-monomer hydrogen bonds. It has also been found that most neutral isomers are capable of excess electron binding to form geometrically and electronically stable anions of dipole-bound nature. The electron binding energies for these anions span a wide region of 0.0004−0.947 eV (depending on the neutral parent molecule). In addition, several cystine-based anions were found at geomet...

Ab initio MRD-CI study on the low-lying excited states of ClNO 2

A theoretical study on the electronic absorption spectrum of nitryl chloride, ClNO 2, has been carried out using multi-reference configuration interaction, MRD-CI, methods with cc-pVDZ + sp and cc-pVTZ + sp basis sets. The electronic spectrum is characterized by two very strong transitions ( f from 0.30 to 0.67 ) at 7.04 eV ( 3 1 A 1← X 1 A 1 ) and 7.25 eV ( 3 1 B 2← X 1 A 1 ). Further, the transition at 5.77 eV ( 2 1 A 1← X 1 A 1 ) is predicted to be somewhat less intense ( f=0.02). In addition, the potential energy curves for the ground and low-lying singlet excited states are examined along the Cl–N bond cleavage. Also, triplet excited states of ClNO 2 are discussed.

Extension of the PDDG/PM3 and PDDG/MNDO semiempirical molecular orbital methods to the halogens.

The new semiempirical methods, PDDG/PM3 and PDDG/MNDO, have been parameterized for halogens. For comparison, the original MNDO and PM3 were also reoptimized for the halogens using the same training set; these modified methods are referred to as MNDO' and PM3'. For 442 halogen-containing molecules, the smallest mean absolute error (MAE) in heats of formation is obtained with PDDG/PM3 (5.6 kcal/mol), followed by PM3' (6.1 kcal/mol), PDDG/MNDO (6.6 kcal/mol), PM3 (8.1 kcal/mol), MNDO' (8.5 kcal/mol), AM1 (11.1 kcal/mol), and MNDO (14.0 kcal/mol). For normal-valent halogen-containing molecules, the PDDG methods also provide improved heats of formation over MNDO/d. Hypervalent compounds were not included in the training set and improvements over the standard NDDO methods with sp basis sets were not obtained. For small haloalkanes, the PDDG methods yield more accurate heats of formation than are obtained from density functional theory (DFT) with the B3LYP and B3PW91 functionals using large basis sets. PDDG/PM3 and PM3' also give improved binding energies over the standard NDDO methods for complexes involving halide anions, and they are competitive with B3LYP/6-311++G(d,p) results including thermal corrections. Among the semiempirical methods studied, PDDG/PM3 also generates the best agreement with high-level ab initio G2 and CCSD(T) intrinsic activation energies for S(N)2 reactions involving methyl halides and halide anions. Finally, the MAEs in ionization potentials, dipole moments, and molecular geometries show that the parameter sets for the PDDG and reoptimized NDDO methods reduce the MAEs in heats of formation without compromising the other important QM observables.

Rayleigh Depolarization Ratios, Kerr Effects, Polarizabilities, and Hyperpolarizabilities of CH3Br, CH2Br2, CHBr3, and CBr4. Comparison of Experimental and ab Initio Calculated Polarizabilities

Improved equipment has been used to record the vapor-phase Rayleigh depolarization ratios and electrooptical Kerr effects of CH3Br, CH2Br2, CHBr3, and CBr4 at elevated temperatures. The measurements yield experimental values of the anisotropic polarizabilities and the Kerr hyperpolarizabilities of these molecules. As well, Dougherty and Spackman's HUZ-SV(+sd+sp) basis set has been used to compute SCF and MP2-level polarizabilities, and these are compared with the experimental results.

Ab initio 2-D periodic Hartree-Fock study of Fe-substituted lizardite 1 T - a simplified cronstedtite model

A 2-D periodic ab initio Hartree–Fock LCAO study was performed on Fe-substituted 1:1 sheet silicate, lizardite. The atomic orbitals were described by large-core pseudopotentials (Fe atoms) and a sp basis set (the other atoms). Calculated atomic charges and the results of bond population analysis indicate that the Fe-O bond was as ionic as the Mg-O. This hypothesis was supported by calculated density of states and electron density maps. Increasing Fe for Mg substitution changed the shape of projected density of states (PDOS) of O(p) orbitals.

A CASSCF–MRCI study on the low-lying excited states of CH3OCl

A theoretical study on the excited states of methylhypochlorite (CH3OCl) has been carried out using high level ab initio molecular orbital methods. The vertical excitation energies for the lowest two A′1 states, three A″1 states, three A′1 states, and three A″1 states are calculated using the multireference configuration interaction (MRCI) method with cc-pVTZ and cc-pVTZ+sp basis sets. In addition, the potential energy curves for the lowest eight states are examined along both the ClO and CO coordinates at the complete active space SCF (CASSCF) level of theory with cc-pVTZ basis set. Except for the ground state, all seven excited states are strongly repulsive along the ClO coordinate, which is in good agreement with recent experimental work. Two absorption bands with maximums at 235 nm and 308 nm in the experimental UV spectra of CH3OCl can be assigned to the transitions X 1A′→1 1A″ and X 1A′→2 1A′.

A CASSCF-MRCI study of the electronic excited states of FClO and FOCl

The potential energy curves for the low-lying excited states of FClO and FOCl have been computed using the complete active space self-consistent field (CASSCF) with cc-pVTZ basis sets. The vertical excitation energies for the excited states were calculated using the multireference configuration interaction (MRCI) method with cc-pVTZ and cc-pVTZ+sp basis sets. The vertical excitation energies were also obtained using the EOM-CCSD (equation of motion-coupled-cluster single double) method with cc-pVTZ basis sets. Results show that Rydberg character is not present in the excited states studied here for both FClO and FOCl. For FClO, all the excited states studied are repulsive along the F–Cl coordinate, but some of the excited states are bound along the Cl–O coordinate. For FOCl, all the excited states studied are dissociative along both the F–O and O–Cl coordinates.

Ab initio calculations ofp-Cl2C6H4 molecule and its35Cl NQR parameters

Ab initio calculations ofp-dichlorobenzene molecule were carried out using the Hartree-Fock method in the 6–31 G* valence-split basis set. The molecule was also calculated by the MNDO method in the valence sp-basis set for comparison. The populations of the valent p-orbitals of the C and CI atoms were analyzed. The optimized geometry of the molecule as well as its35Cl NQR frequency and the asymmetry parameter of the electric field gradient at the35CI nuclei calculated using the populations of the less diffuse components of the valent p-orbitals of the Cl atoms are in agreement with the corresponding experimental values for the α-modification of 1,4-Cl2C6H4.

Molecular Polarizability as a Tool for Understanding the Binding Properties of Polychlorinated Dibenzo-p-Dioxins: Definition of a Reliable Computational Procedure

Molecular polarizability can be used to gain an insight into the origins of polychlorinated dibenzo-p-dioxins (PCDDs) specific binding to their receptor protein. In this work, the effects of the basis set on the polarizability values calculated at the HF level of benzene, chlorobenzene, and dibenzo-p-dioxin (DD) are analyzed. The geometry optimized with the 3-21G basis set and polarizability calculated with the 6-31G(sd,sp) basis set give reliable values useful for comparing polarizabilities of PCDDs with reduced computational costs. The study for two tetrachlorodibenzo-p-dioxin isomers highlights interesting differences in the molecular polarizability tensors as well as in the polarizabilities of C−Cl bonds related to the different chlorine positions on the aromatic skeleton.

Numerical multiconfigurational Hartree–Fock calculations of spin and charge densities using the Hiller–Sucher–Feinberg operator identity

The Hiller–Sucher–Feinberg operator has been implemented into the atomic finite-element multiconfiguration spin-restricted Hartree–Fock program lucas. The spin-dependent and spin-independent Hiller–Sucher–Feinberg operators have been tested on Li(2Se), Be(3Po), B(2Po), C(3Pe), N(4So), O(3Pe), and F(2Po) using numerical and Gaussian sp basis sets. In the basis-set calculations, the electron-charge densities at the nucleus obtained using the Hiller–Sucher–Feinberg operator are about 50 times more accurate than the values obtained using the δ-function operator. In the numerical correlation calculations, the spin densities at the nucleus obtained for Li, C, N, O, and F using the Hiller–Sucher–Feinberg operator converge faster with the size of the orbital space than those obtained using the δ-function operator, and for Be and B, the two spin-dependent operators perform about equally well.

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.

Ab initio studies of the dipole polarizabilities of conjugated molecules: Part 2. Monocyclic azines

We report high quality ab initio calculations of the dipole polarizability and first hyperpolarizability of the following single monoeyclic azines: pyridine, pyridazine, pyrimidine, pyrazine, s-triazine and s-tetrazine. A study of the sensitivity of such calculated properties to the variation of basis set shows that increasing the number of multiple d and p diffuse functions in the 6-31 + G( nd, mp) basis set at Hartree-Fock level gives values of the polarizability tensor components that are comparable with the experimental ones, and consistent values of hyperpolarizability tensor components. We have also found that correlation effects are negligible, provided that such calculations are performed at the SCF level with very extended basis sets. We show that standard sp basis sets need to be extended in the sp space, to have extra diffuse functions added and also to include suitable d and p gaussian primitives in order to be useful for the calculation of response functions. We find that the average dipole polarizability (α ave) is related to the number of nitrogen atoms N in the ring by α ave/10 −40(CV −1 m 2) = 10.90–0.90 N We also find that the calculated average and anisotropy polarizability components are both linearly related to the sum of the HOMO and LUMO orbital energies. We also give the first ever high-quality calculation of the hyperpolarizability tensors for these molecules. Electric dipole and quadrupole moments agree well with experiment, as do the asymmetry parameter and the nitrogen quadrupole coupling constants.

A theoretical investigation of the geometries, vibrational frequencies, and binding energies of several alkali halide dimers

Results are presented from ab initio calculations on the symmetrical alkali halide dimers made up of Li, Na, K, F, and Cl. We examine the sensitivity of representative monomer and dimer geometries to the variation of the basis set with and without polarization and diffuse functions. The geometries are then compared with available experimental results. We have also calculated vibrational frequencies at the restricted Hartree–Fock level and examined the changes in geometry brought about by correlation using second-order Mo/ller–Plesset perturbation theory. It is found that Hartree–Fock theory in a modest basis set with diffuse and polarization functions yields results comparable to much larger sp basis sets and that the theoretical results are in good agreement with the experimental results for the Li and Na dimers. Our best results for the K-containing species tend to have bond lengths that are too long for the monomers and this error is carried over for the dimers. We also find a nearly uniform expansion of the M–X bond length in proceeding from monomer to dimer of 0.16±0.03 Å, independent of the alkali or halide involved. The calculated dimer dissociation energies are in excellent agreement with experiment. Inclusion of correlation appears to have a minimal effect on the computed geometries and a modest effect on the binding energies. The vibrational frequencies for the monomers are in excellent agreement with experimental gas-phase results and reasonable agreement is obtained with the available experimental frequencies for the dimers. Finally, a reanalysis of the electron diffraction data for Na2F2 in light of the current ab initio results leads to a significant change in the experimental value of the bond angle.

A new tight binding parameterization for carbon

Working within a minimal orbital sp basis set with fixed site energies and a repulsive pairwise interaction the author fits a set of hopping integrals and a repulsive pair potential to experimental graphite and diamond band structures, binding energies, lattice constants and bulk moduli, and to accurate local density functional data for the binding energies and equilibrium volumes of face centred cubic, simple cubic and beta tin phases of carbon. He finds that an approximately inverse cube form for the hopping integrals as a function of interatomic separation and an approximately inverse nine-halves power for the air potential leads to an improved fit to the data including the band structure of graphite. Both the hopping integrals and the pair potential are seen to decay more rapidly than similar parameters for silicon, reflecting the absence of nuclear screening by core electron states.

Time-dependent Hartree–Fock second-order molecular properties with a moderately sized basis set. II. Dispersion coefficients

Time-dependent coupled Hartree–Fock frequency-dependent polarizabilities are used to obtain ab initio dipole–dipole C6, dipole–quadrupole C8, and triple–dipole ν, dispersion coefficients. The moderately sized 6-31G (+sd+sp) basis set optimized for calculation of molecular static dipole polarizabilities has enabled the computation of dispersion coefficients for a wide variety of molecules containing atoms up to chlorine. Results are presented for 48 molecules including benzene, cyclohexane, SF6, and CCl4. Appropriate scaling of 6-31G(+sd+sp) results for C6 and ν enables the prediction of these coefficients to within 3% of experimental estimates that are based on dipole oscillator strength distributions. Results for the mean static quadrupole polarizability C̄(0) and C8 dispersion coefficient are presented for nondipolar molecules and the origin dependence of C8 is investigated.

Time-dependent Hartree–Fock second-order molecular properties with a moderately sized basis set. I. The frequency dependence of the dipole polarizability

Time-dependent coupled Hartree–Fock calculations of the frequency-dependent mean polarizability α(ω) and its anisotropy Δα(ω) are presented for a wide range of molecules containing first and second row atoms. The Cauchy moments S(−2) and S(−4), which describe the dispersion in α(ω), are systematically underestimated by 20% and 40%, respectively, with the 6-31G(+sd+sp) basis set. The dispersion in Δα(ω) is also underestimated, typically by 50%. Many exceptions to this behavior are observed, most of which appear to be an underestimate of the experimental dispersion in Δα(ω) by a greater amount. This seems to be the result of systematic experimental overestimates of dispersion in Δα(ω) for molecules with very small Rayleigh depolarization ratios (ρ0&amp;lt;10−2), suggesting that the vibrational Raman contribution in these experiments is not only important, but significantly frequency dependent.