Maximum radius of convergence perturbation theory: test calculations on Be,Ne, H<Subscript>2</Subscript> and HF

Maximum radius of convergence (MAXR _c) perturbation theory [(2000) Journal of Chemical Physics 112:6997] is tested on the beryllium and neon atoms using calculations that are truncated in high orders. Calculations are also performed on the ground-state potential-energy curves of H₂ and HF. The neon atom calculations use the 3-21G basis set with added diffuse s and p functions. All other calculations use the STO-3G minimum basis set. MAXR _c perturbation theory consistently performs well. The Epstein–Nesbet and Møller–Plesset perturbative expansions frequently diverge or exhibit slow convergence compared to the expansions obtained from MAXR _c. AcknowledgementsJ.P. Fi. acknowledges support for a grant from the Japanese Society for the Promotion of Science.Contribution to the Björn Roos Honorary Issue     

Effects of global orbital cutoff value and numerical basis set size on accuracies of theoretical atomization energies

Numerical basis sets are known for their rapid convergence in density functional theory calculations. The selections of global orbital cutoff values and numerical basis set sizes are important to the computational accuracies and efficiencies. In this study, the effects of global orbital cutoff values and numerical basis set sizes on the theoretical atomization energies (D ₀) were investigated using density functional theory with the generalized gradient approximation. Our results on the total energies of seven atoms and D ₀ of a set of 44 molecules demonstrate that the numerical orbital cutoff value should be larger than 6.5 Å to get the converged energetic properties. Through comparing the D ₀ of these 44 molecules obtained by using four kinds of different numerical basis sets, DN, DND, DNP, and TNP, it demonstrates that the DNP basis set is good enough to predict accurate D ₀ with affordable computational cost.     

An analysis of SCF and geometry convergence for diatomic molecules

A geometry and SCF convergence study of Hartree-Fock calculations using the 6-31G* basis set is carried out on the set of all possible diatomic molecules formed from atoms with Z≤36. The utility of Hartree-Fock calculations using the smaller STO-3G basis set to improve the convergence behavior is demonstrated.      

Geometry optimization and electronic structures of molecules H_3AXAH_3

The geometries of molecules H_3AXAH_3(X=O,S,Se and A=C,Si)have been optimizedusing STO-3G ab initio calculations and gradient method and the results are in good agreement withreported experimental values.From the STO-3G optimized geometries,we have also calculated theelectronic structures of these molecules using 4-31G and 6-31G basis sets to obtain the MO energies.atomic net charges and dipole moments.The ionization potentials calculated by 6-31G basis set are ingood agreement with experimental values.     

Oxygen-induced next-nearest neighbour effects on the C1s-levels in polymer XPS-spectra

This letter reports the results of ab initio quantum chemical calculations on the C_1s core levels of model systems for a number of oxygen containing polymers. Conformational effects were studied. SCF calculations have been carried out with STO-3G and 4-31G basis sets, and Koopmans' theorem was applied to obtain the core-level binding energies. To evaluate the performance of the procedure SCF calculations were carried out on polyacrylic acid. The existence of oxygen-induced secondary substituent effects in the XPS-(ESCA-)spectra is discussed. A comparison with semi-empirical CNDO/2 results from Clark and Thomas has been made.     

Ab initio valence bond calculations and the spin-paired diradical character of S 4 2+

The results of some ab initio valence bond calculations, with STO-6G basis sets for the s and p orbitals, are reported for the ground state of cyclic S ₄ ²⁺ . The sum of the weights for two long-bond (or spin-paired diradical) structures is approximately 50% of the total.     

Ab initio studies on several species of the formula X3YO and X3YOH

Ab initio molecular orbital calculations using both minimal and extended basis sets have been applied to two isoelectronic sets of molecules. One set corresponds to the 18 electron species H₃NO, H₃CO^– and H₃COH while the second set contains the 42 electron fluorinated molecules F₃NO, F₃CO^– and F₃COH. The geometries of these molecules have been optimized, using both the minimal STO-3G and the extended 4-31G basis sets. These comparative calculations reveal that the 4-31G basis produced structural parameters in much better agreement with experiment. The effect of includingd-orbitals in the basis set was also investigated. For the fluorinated oxides it has been found that the optimized 4-31G structures were only slightly altered by the addition ofd-orbitals. For H₃NO, on the other hand, the inclusion ofd-orbitals considerably shortens the N-O bond distance. Both H₃NO and CF₃OH, which are unknown experimentally, are theoretically predicted to be capable of existence. The electronic structures of these molecules have also been examined using electronic partitioning according to the Mulliken scheme.     

H2O,H2, HF,F2 and F2O nuclear magnetic shielding constants and indirect nuclear spin–spin coupling constants (SSCCs) in the BHandH/pcJ‐n and BHandH/XZP Kohn–Sham limits

Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H₂O, H₂, HF, F₂ and F₂O nuclear isotropic shielding constants in the BHandH Kohn–Sham basis set limit was shown. The results of two‐ and three‐parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization‐consistent basis sets pcS‐n and pcJ‐n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were more sensitive to the XZP basis set size and generally less accurate than those estimated using pcJ‐n basis set family. The BHandH density functional markedly outperforms B3LYP method in predicting heavy atom shieldings and SSCCs values in the studied systems. Copyright © 2009 John Wiley & Sons, Ltd.     

The electronic structure of small lithium clusters

Ab initio molecular orbital calculations using the STO-6G and STO6-21G basis sets have been performed for the cluster series Li _n ⁺ , Li _n , and Li _n ^– (wheren=2–7). Thirty-two optimized structures are discussed and reported, many of which (especially for the anionic structures) have not yet been considered. The calculations suggest that for all three species the optimum geometries are planar. Of the two levels of theories that were investigated, STO-6G//STO-6G and STO6-21G//STO-6G, the latter hybrid theory was found to be less reliable. In particular, for the anionic structures these calculations should provide a platform from which more sophisticated, i.e., configuration interaction, geometry optimization can be performed.     

A charge-conserving approximation method for ab initio calculations

A new method is presented for approximate ab initio calculations in quantum chemistry. It is called CCAM (charge conserving approximation method). The calculation method does not include the use of empirical parameters. We use Slater type orbitals as basis set, replacing STO's by STO-2G functions to evaluate three- and four-center integrals and making the STO-2G two-orbital charge distributions have the same total charge as STO. The results are presented for test calculations on five molecules. In view of these results, CCAM is better than ab initio calculations over STO-6G in the results on total energies, kinetic energies and occupied orbital energies. In atomic populations, dipole moments and unoccupied orbital energies, CCAM is also satisfactory. We estimate that CCAM would be as fast as ab initio calculations over STO-2G in evaluating molecular integrals.     

Theoretical study of the electronic structure of diazomethane

The least-energy dissociation path of the ground state of CH₂N₂ was determined fromab initio calculations using in a complementary way basis sets of minimal size (STO-3G) and double-zeta (DZ) quality. The results indicate that the least-energy point of attack of the N₂ molecule on CH₂ (¹ A ₁) is roughly perpendicular to the molecular plane (93 °), the C and N atoms being almost co-linear (angle C-N-N203 ° with outermost N atom pointing away from CH₂). The potential barrier of 1.2 eV found previously on theC _2v dissociation path, disappears completely along the least-energy dissociation path (point groupC _s (out-of-plane)). These findings corroborate the Woodward-Hoffman rules for this process since the outermost orbitals of the two intersecting states found in point groupC _2v (...2b ₁ and ...8a ₁) both correlate to the same irreducible representation (10á) in point groupC _s (out-of-plane).Larger basis set calculations (DZ + polarization functions on all centers, 3d _c and 3d _N developed here), were also carried out on CH₂N₂ (¹ A ₁,³ A ₂ and¹ A ₂) at the¹ A ₁ equilibrium geometry and on CH₂ (³ B ₁) and N₂ (¹ _g ⁺ ) at their respective equilibrium geometries. These calculations, together with consideration of correlation energy differences, yieldD ₀ ⁰ (CH₂N₂,¹ A ₁) = 19 kcal/mole and vertical excitation energies of 67 and 73 kcal/mole for the³ A ₂ and¹ A ₂ states respectively. The latter value is in good agreement with the measured experimental value: 72.4 kcal/mole corresponding to the maximum of intensity in the¹ A ₂¹ A ₁ absorption band.     

Computational schemes for modeling proton transfer in biological systems: Calculations on the hydrogen bonded complex [CH3OH · H · NH3]+

Different schemes are explored for the calculation of the proton transfer process in the hydrogen bonded cation [CH₃OH · H · NH₃]⁺. Results from ab-initio calculations with the STO-3G, 3-21G and 4-31G basis sets, are compared in search for an efficient reliable scheme to study the potential energy curves for the proton transfer. The curve constructed from the lowest energies calculated with the frozen optimized geometries of the two possible pairs of proton donor and acceptor fragments, (i.e., CH₃OH/NH₃ and CH₃OH/NH) is in good agreement with that obtained when all the fragments of the hydrogen bonded complex are completely optimized simultaneously.     

Theoretical Modeling of the Stereoisomerization of Tetracoordinated Be(II) Bis(chelate) Complexes

Quantum-chemical (semiempirical MNDO and ab initio RHF SCF with an STO-3G basis set) calculations were performed for stereoisomerization of tetracoordinated Be(II) bis(chelate) complexes with BeN₂O₂ coordination unit. The most probable pathway for their monomolecular isomerization was found to involve, in agreement with experimental data, cleavage of a Be–N coordination bond to form a tricoordinated Be intermediate (dissociation–recombination mechanism) rather than a competitive polytopal rearrangement. The planar structure of the intermediate detected upon thermo- and photoexcitation of the complexes was predicted from our calculations.     

Isolobal analogy between trivalent boron and divalent silicon

Singlet organosilylenes with a lone pair and an emptyp orbital are isolobal to trivalent borane if a B-H is equated to the lone pair on Si. Using this analogy, a particular isomer of CSi₂H₂ (24) is predicted to be a stable structure. MNDO calculations on24 and many of its possible isomers suggest that24 is at global minimum on the potential energy surface of CSi₂H₂.Ab initio calculations using a, minimal STO-3G basis set, on some selected structures also support these results.     

Ab initio SCF calculations on hydrogen bonded cresol isomers

Ab initio GAUSSIAN 80 calculations with two different basis sets (STO-3G and 4–31 G*) were performed on hydrogen bonded cresol isomers for comparison with experimental data from free jet fluorescence excitation spectroscopy. Form-cresol, the calculated barriers for hindered internal rotation of the OH-group and the CH₃-group are in good agreement with experiment. The calculations show the trans-linear configuration ofp-cresol·B-clusters (B = H₂O, CH₃OH) to be more stable than the all-planar configuration. This agrees with CI calculations and microwave spectroscopic investigations of the water dimer. Calculations of both the intermolecular stretch and bend frequencies ofp-cresol·B-clusters show little dependence on the all-planar or trans-linear configuration but a strong dependence on the choice of the basis set. With the minimal basis set STO-3G, the vibrational energies are generally too high. The agreement between the calculated vibrational frequencies from the 4–31 G* basis set and the experimental values is fair.     

Crystallographic studies of intra- and intermolecular interactions. Part 4. A comparative study of the effect of through-resonance on the geometry of p-nitro- and p-nitrosophenolate anions

The VB- and the HOSE-model calculations carried out on the basis of an experimental geometry of p-nitro- and p-nitrosophenolate anions revealed that the NO₂ group is a much weaker-electron acceptor than the NO group. The STO-3G ab initio calculation with optimization of the geometry supported this view. Electrochemical study in an aprotic solvent (DMF) yielded estimates of electron affinity for nitro- and nitrosobenzene and indicated a much lower value for the latter, supporting stronger electron accepting properties of the NO group in p-X-Ph-NO systems with X-electron donating substitutents. -electron distribution in p-nitrosophenolate anions depends strongly on H-bonding interactions in a crystal lattice as deduced directly from the HOSE-model and the VB calculations for the experimental geometry.     

Static hyperpolarizability of the van der Waals complex CH4?N2

The static first hyperpolarizability of the van der Waals CH₄ N₂ complex was calculated. The calculations were carried out in the approximation of the rigid interacting molecules for a broad range of intermolecular separations (R = 6–40 a₀) and for six configurations at CCSD(T) level of theory using the correlation consistent aug-cc-pVTZ basis set with the basis set superposition error correction. It was shown that the long-range classical approximation, including the terms up to R⁻⁶, is in a good agreement with ab initio calculations for R > 11 a₀. It was found out that for the family of most stable configurations of the complex, the first hyperpolarizability invariants practically do not change (the changes are less than 0.1%). Under forming the stable van der Waals CH₄ N₂ complex, the intensity and degree of depolarization of the hyper-Rayleigh scattering are noticeable decreased (by ∼10%) to be compared with the free CH₄ and N₂ molecules. © 2012 Wiley Periodicals, Inc.     

Determination of ab initio polarizabilities of polymers: Application to polyethylene and polysilane

An ab initio method for calculating the longitudinal linear polarizability of polymeric chains is described. This method is equivalent to an uncoupled Hartree–Fock scheme. It is applied to polyethylene and polysilane in minimal STO-3G and extended 4-31G basis sets. The study describes important techniques for solving the difficulties met in actual calculations: band reordering of the band structures, calculation of analytical derivatives of the energy bands ?_n(k) and LCAO coefficients c_np(k), and errors caused by the improper lattice sum truncations of the Hartree–Fock matrix.