Influence of diffuse and polarization functions on the second-order Møller–Plesset optimized dihedral angle of biphenyl

 Using 6-31G and 6-311G basis sets to which diffuse and polarization functions were added in a stepwise fashion (a total of 16 basis sets), Hartree–Fock (HF), MP2 and B3LYP geometry optimizations were performed on biphenyl. With the MP2 method, diffuse functions raise the dihedral angle φ, for example, from 46.3° for 6-31G to 54.1° for 6-311++G, while polarization functions lower it, for example, from 54.1° for 6-311++G to 42.1° for 6-311++G(2d,2p). For a single set of polarization functions, φ(MP2) lies close to or above φ(HF) (44–47°), but for a double set it is below φ(HF) and is close to B3LYP values (38–42°) which show little basis set dependence. The most reliable value for φ, 42.1° [MP2/6-311++G(2d,2p)], is expected to increase slightly by adding more diffuse functions. The corresponding best calculated energy barrier at 0° (coplanar conformation) is 2.83 kcal/mol, much higher than the experimental estimate (1.4 ± 0.5 kcal/mol). The barrier at 90° is 1.82 kcal/mol, in line with the experimental estimate (1.6 ± 0.5 kcal/mol) and with previous theoretical results. Received: 9 September 2002 / Accepted: 15 November 2002 / Published online: 1 April 2003 Correspondence to: Friedrich Grein e-mail: fritz@unb.ca Acknowledgement. The author would like to thank NSERC (Canada) for financial support.     

The performance of the rapid estimation of basis set error and correlation energy from partial charges method on new molecules of the G3/99 test set

Experimental enthalpies of formation have been approximated using single-point Hartree–Fock (HF)–self-consistent-field (SCF) total energies plus the rapid estimation of basis set error and correlation energy from partial charges (REBECEP) energy corrections. The energy corrections are calculated from the HF–SCF partial atomic charges and optimized atomic energy parameters. The performance of the method was tested on 51 closed-shell neutral molecules (50 molecules from the G3/99 thermochemistry database plus urea, composed of H, C, N, O, and F atoms). The predictive force of the method is demonstrated, because these larger molecules were not used for the optimization of the atomic parameters. We used the earlier RECEP-3 [HF/6-311+G(2d,p)] and REBECEP [HF/6-31G(d)] atomic parameter sets obtained from the G2/97 thermochemistry database (containing small molecules) together with natural population analysis and Mulliken partial charges. The best results were obtained using the natural population analysis charges, although the Mulliken charges also provide useful results. The root-mean-square deviations from the experimental enthalpies of formation for the selected 51 molecules are 1.15, 3.96, and 2.92 kcal/mol for Gaussian-3, B3LYP/6-11+G(3df,2p), and REBECEP (natural population analysis) enthalpies of formation, respectively (the corresponding average absolute deviations are 0.94, 7.09, and 2.27 kcal/mol, respectively). The REBECEP method performs considerably better for the 51 test molecules with a moderate 6-31G(d) basis set than the B3LYP method with a large 6-311+G(3df,2p) basis set. Received: 10 March 2001 / Accepted: 5 July 2001 / Published online: 11 October 2001     

Use of addition theorems in evaluation of multicenter nuclear-attraction and electron-repulsion integrals with integer and noninteger n Slater-type orbitals

Multicenter integrals appearing in the Hartree–Fock–Roothaan equations for molecules are calculated using different kinds of series expansion formulas obtained from the expansions of integer and noninteger n Slater-type orbitals, in terms of Ψ ^α -exponential-type orbitals (where α=1, 0, –1, –2,...) at a displaced center, that form complete orthonormal sets and are represented by linear combinations of integer n Slater-type orbitals. The convergence of these series is tested by calculating concrete cases. The accuracy of the results is quite high for quantum numbers, screening constants, and location of orbitals. Received: 13 February 2002 / Accepted: 11 March 2002 / Published online: 4 July 2002     

Dipole–reaction field interaction model for the solvent reorganization energy and its application to the benzoquinone–benzoquinone anion radical system

 Based on the spherical cavity approximation and the Onsager model, a dipole–reaction field interaction model has been proposed to elucidate the solvent reorganization energy of electron transfer (ET). This treatment only needs the cavity radius and the solute dipole moment in the evaluation of the solvent reorganization energy, and fits spherelike systems well. As an application, the ET reaction between p-benzoquinone and its anion radical has been investigated. The inner reorganization energy has been calculated at the level of MP2/6–31+G, and the solvent reorganization energies of different conformations have been evaluated by using the self-consistent reaction field approach at the HF/6–31+G level. Discussions have been made on the cavity radii and the values are found to be reasonable when compared with the experimental ones of some analogous intramolecular ET reactions. The ET matrix element has been determined on the basis of the two-state model. The fact that the value of the ET matrix element is about 10 times larger than RT indicates that this ET reaction can be treated as an adiabatic one. By invoking the classical Marcus ET model, a value of 4.9 × 10⁷M⁻¹s⁻¹ was obtained for the second-order rate constant, and it agrees quite well with the experimental one. Received: 19 October 2001 / Accepted: 17 January 2002 / Published online: 3 May 2002     

Internal rotation in squaramide and related compounds. A theoretical ab initio study

The structural and energetic changes associated with C–N bond rotation in a squaric acid derivative as well as in formamide, 3-aminoacrolein and vinylamine have been studied theoretically using ab initio molecular orbital methods. Geometry optimizations at the MP2(full)/6-31+G* level confirmed an increase in the C–N bond length and a smaller decrease in the C=O length on going from the equilibrium geometry to the twisted transition state. Other geometrical changes are also discussed. Energies calculated at the QCISD(T)/6-311+G** level, including zero-point-energy correction, show barrier heights decreasing in the order formamide, squaric acid derivative, 3-aminoacrolein and vinylamine. The origin of the barriers were examined using the atoms-in-molecules approach of Bader and the natural bond orbital population analysis. The calculations agree with Pauling's resonance model, and the main contributing factor of the barrier is assigned to the loss of conjugation on rotating the C–N bond. Finally, molecular interaction potential calculations were used to study the changes in the nucleophilicity of N and O (carbonyl) atoms upon C–N rotation, and to obtain a picture of the abilities of the molecules to act in nonbonded interactions, in particular hydrogen bonds. The molecular interaction potential results confirm the suitability of squaramide units for acting as binding units in host–guest chemistry. Received: 13 March 2002 / Accepted: 23 June 2002 / Published online: 21 August 2002     

Improved generator coordinate Hartree–Fock method for molecular systems: application to H2, Li2 and LiH

The improved generator coordinate Hartree–Fock (GCHF) method is extended to molecular systems. The Griffin–Hill–Wheeler–HF equations were solved by an integral discretization technique. The method is then implemented with the use of the GAMESS program and applied to the H₂, Li₂, and LiH molecules. For these molecules, sequences of basis sets of atom-centred Gaussian-type functions are employed to explore the accuracy achieved with our approach. For all systems studied, our ground-state HF total energies are better than those obtained with basis sets generated with the original GCHF method for molecules and larger even-tempered basis sets. For H₂, Li₂, and LiH, the differences between our best energies and the corresponding numerical HF results are about 2 × 10⁻², 1, and 4 × 10⁻¹ μhartree, respectively. The dipole, quadrupole, and octupole moments at the center of mass and electric field, the electric field gradient, the electrostatic potential, and the electron density at the nuclei were evaluated and compared with results reported in the literature. Received: 4 May 1999 / Accepted: 22 July 1999 / Published online: 2 November 1999     

An atom-in-molecules and electron-localization-function study of the interaction between O2 and VxOy+/VxOy (x = 1, 2, y = 1–5) clusters

 The most stable structures of V _x O _y ⁺/V _x O _y (x=1, 2, y=1–5) clusters and their interaction with O₂ are determined by density functional calculations, the B3LYP functional with the 6-31G* basis set. The nature of the bonding of these clusters and the interaction with O₂ have been studied by topological analysis in the framework of both the atoms-in-molecules theory of Bader and the Becke–Edgecombe electron localization function. Bond critical points are localized by means of the analysis of the electron density gradient field, ∇ρ(r), and the electron localization function gradient field, ∇η(r). The values of the electron density properties, i.e., electron density, ρ(r), Laplacian of the electron density, ∇²ρ(r), and electron localization function, η(r), allow the nature of the bonds to be characterized, and linear correlation is found for the results obtained in both gradient fields. Vanadium-oxygen interactions are characterized as unshared-electron interactions, and linear correlation is observed between the electron density properties and the V–O bond length. In contrast, O₂ units involve typical shared-electron interactions, as for the dioxygen molecule. Four different vanadium–oxygen interactions are found and characterized: a molecular O₂ interaction, a peroxo O₂ ²⁻ interaction, a superoxo O₂ ⁻ interaction and a side-on O₂ ⁻ interaction. Received: 15 October 2001 / Accepted: 30 January 2002 / Published online: 24 June 2002     

Isotope effect of hydrogen and lithium hydride molecules. Application of the dynamic extended molecular orbital method and energy component analysis

In order to explore the isotope effect including the nuclear–electronic coupling and nuclear quantum effects under the one-particle approximation, we apply the dynamic extended molecular orbital (DEMO) method and energy component analysis to the hydrogen and lithium hydride isotope molecules. Since the DEMO method determines both electronic and nuclear wave functions simultaneously by variationally optimizing all parameters embedded in the basis sets, the virial theorem is completely satisfied and guarantees the relation of the kinetic and potential energies. We confirm the isotope effect on internuclear distances, nuclear and electronic wave functions, dipole moment, the polarizability, and each energy component. In the case of isotopic species of the hydrogen molecule, the total energy decreases from the H₂ to the T₂ molecule due to the stabilization of the nuclear–electronic potential component, as well as the nuclear kinetic one. In the case of the lithium hydride molecule, the energy lowering by replacing ⁶Li with ⁷Li is calculated to be greater than that by replacing H with D. This is mainly caused by the small destabilization of electron–electron and nuclear–nuclear repulsion in ⁷LiH compared to ⁶LiH, while the change in the repulsive components from ⁶LiH to ⁶LiD increases. Received: 24 March 1999 / Accepted: 5 August 1999 / Published online: 15 December 1999     

Computational structural determination and energy landscape analysis of the hepatic carcinogen 2-(acetylamino)fluorene

 2-(Acetylamino)fluorene (AAF), a potent mutagen and a prototypical example of the mutagenic aromatic amines, forms covalent adducts to DNA after metabolic activation in the liver. A benchmark study of AAF is presented using a number of the most widely used molecular mechanics and semiempirical computational methods and models. The results are compared to higher-level quantum calculations and to experimentally obtained crystal structures. Hydrogen bonding between AAF molecules in the crystal phase complicates the direct comparison of gas-phase theoretical calculations with experiment, so Hartree–Fock (HF) and Becke–Perdew (BP) density functional theory (DFT) calculations are used as benchmarks for the semiempirical and molecular mechanics results. Systematic conformer searches and dihedral energy landscapes were carried out for AAF using the SYBYL and MMFF94 molecular mechanics force fields; the AM1, PM3 and MNDO semiempirical quantum mechanics methods; HF using the 3-21G*and 6-31G* basis sets; and DFT using the nonlocal BP functional and double numerical polarization basis sets. MMFF94, AM1, HF and DFT calculations all predict the same planar structures, whereas SYBYL, MNDO and PM3 all predict various nonplanar geometries. The AM1 energy landscape is in substantial agreement with HF and DFT predictions; MMFF94 is qualitatively similar to HF and DFT; and the MNDO, PM3 and SYBYL results are qualitatively different from the HF and DFT results and from each other. These results are attributed to deficiencies in MNDO, PM3 and SYBYL. The MNDO, PM3 and SYBYL models may be unreliable for compounds in which an amide group is immediately adjacent to an aromatic ring. Received: 26 May 2002 / Accepted: 12 December 2002 / Published online: 14 February 2003     

An investigation of basis set effects in the characterization of electron – atom scattering resonances using the dilated electron propagator method

 The effects of basis set variations on resonance attributes are investigated using systematically augmented basis sets by correlating the resulting changes in resonance energy and width with the alterations induced in the radial probability density profile of the resonant orbital. Applications to ²P Be⁻ and ²P Mg⁻ shape resonances reveal that basis sets capable of describing both electron density accumulation near the target nucleus to facilitate resonance formation and sufficiently large electron density away from the target nucleus to provide for its decay are necessary for effective characterization of these resonances. A comparison of radial probability density profiles from the bivariational self-consistent field, the second-order, the diagonal two particle–one hole Tamm–Dancoff approximation and quasiparticle decouplings reveals that relaxation effects dominate in resonance formation. Received: 3 January 2000 / Accepted: 5 March 2000 / Published online: 21 June 2000     

Pseudopotential study of lanthanum and lutetium dimers

Relativistic energy-consistent small-core lanthanide pseudopotentials of the Stuttgart–Bonn variety and extended valence basis sets have been used for the investigation of the dimers La₂ and Lu₂. It was found that the ground states for La₂ and Lu₂ are most likely ¹∑ _g ⁺ (σ _g ²π _u ⁴) and ³∑ _g ⁻ (4f ¹⁴4f ¹⁴σ _g ²σ _u ²π_u ²), respectively. The molecular constants including error bars were derived from multireference configuration interaction as well as coupled-cluster calculations, taking into account corrections for atomic spin–orbit splitting as well as possible basis set superposition errors. The theoretical values for La₂ (R _e=2.70±0.03 ?, D _e=2.31±0.13 eV, ω_e=186±13 cm⁻¹) show good agreement with the experimental binding energy (D _e=2.52±0.22 eV), but the experimental vibrational constant in an Ar matrix (ω_e=236±0.8 cm⁻¹) is significantly higher. For Lu₂ the theoretical values (R _e=3.07±0.03 ?, D _e=1.40±0.12 eV, ω_e=123±1 cm⁻¹) are in overall excellent agreement with experimental data (D _e=1.43±0.34 eV, ω_e=122± 1 cm⁻¹). The electronic structures of La₂ and Lu₂ are compared to those other lanthanide dimers and trends in the series are discussed. Received: 25 March 2002 / Accepted: 2 June 2002 / Published online: 21 August 2002     

Evaluation of the Coulomb energy in relativistic self-consistent-field theory

 Computational schemes are presented with which to evaluate the electrostatic Coulomb energy in relativistic molecular electronic structure calculations using a basis of four-component Dirac spinor amplitudes. We demonstrate that algorithms may be constructed and implemented which differ only in minor details from those in common use in nonrelativistic quantum chemistry, and that the four-component formalism is neither as complicated nor as expensive as has been suggested recently in the literature. Spherically symmetrical atomic basis sets are presented which indicate that accurate representations of the Coulomb energy may be obtained using modest expansions of the electronic density in a scalar auxiliary basis set of spherical harmonic Gaussian-type functions. Received: 15 April 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002     

The calculation of electron localization and delocalization indices at the Hartree–Fock, density functional and post-Hartree–Fock levels of theory

 Localization, λ(A), and delocalization indices, δ(A,B), as defined in the atoms in molecules theory, are a convenient tool for the analysis of molecular electronic structure from an electron-pair perspective. These indices can be calculated at any level of theory, provided that first- and second-order electron densities are available. In particular, calculations at the Hartree–Fock (HF) and configuration interaction (CI) levels have been previously reported for many molecules. However, λ(A) and δ(A,B) cannot be calculated exactly in the framework of Kohn–Sham (KS) density functional theory (DFT), where the electron-pair density is not defined. As a practical workaround, one can derive a HF-like electron-pair density from the KS orbitals and calculate approximate localization and delocalization indices at the DFT level. Recently, several calculations using this approach have been reported. Here we present HF, CI and approximate DFT calculations of λ(A) and δ(A,B) values for a number of molecules. Furthermore, we also perform approximate CI calculations using the HF formalism to obtain the electron-pair density. In general, the approximate DFT and CI results are closer to the HF results than to the CI ones. Indeed, the approximate calculations take into account Coulomb electron correlation effects on the first-order electron density but not on the electron-pair density. In summary, approximate DFT and CI localization and delocalization indices are easy to calculate and can be useful in the analysis of molecular electronic structure; however, one should take into account that this approximation increases systematically the delocalization between covalently bonded atoms, with respect to the exact CI results. Received: 13 February 2002 / Accepted: 24 April 2002 / Published online: 18 June 2002     

A DFT study of pyramidalized alkenes: 7-oxasesquinorbornenes and 7,7′-dioxasesquinorbornenes

  DFT calculations of 7′–oxasesquinorbornenes and 7,7′-dioxasesquinorbornenes using the B3LYP/6–31G* method are reported. All the investigated structures (syn- and anti- derivatives) showed significant non-planarity of the central double bond, with the exception of those anti-derivatives possessing symmetrical structures. The influence of the replacement of the methylene groups at position 7- of the norbornene fragment with oxygen and the introduction of second and third (peripheral) double bonds and benzene rings on the molecular and electronic structures of these molecules have also been investigated. Received: 11 November 2002 / Accepted: 6 June 2002 / Published online: 29 April 2003     

Ab initio and density functional theory studies on the mechanism of nucleophilic vinylic substitution of 4<Emphasis Type="Italic">H</Emphasis>-pyran-4-one and 2-methyl-4<Emphasis Type="Italic">H</Emphasis>-pyran-4-one with ammonia

 Nucleophilic vinylic substitutions of 4H-pyran-4-one and 2-methyl-4H-pyran-4-one with ammonia were calculated by the B3LYP method using the 6-31G(d,p) basis set. Bulk solvent effects of aqueous solution were estimated by the polarized continuum and Poisson–Boltzmann self-consistent reaction field models using the 6-311+G(d,p) basis set. In the gas phase different mechanisms were found for the two reaction systems calculated. The reaction of 4H-pyran-4-one proceeds through enol, whereas a feasible path for the less reactive 2-methyl-4H-pyran-4-one is the mechanism through a keto intermediate. Addition of ammonia in concert with proton transfer is the rate-determining step ofthe reaction. The mechanism proceeding either by a bimolecular nucleophilic substitution (S_N2) or by one involving a tetrahedral zwitterionic intermediate is shown to be unlikely in the gas phase or nonpolar solution. The effects of bulk solvent not only consist in a reduction of the various activation barriers by about 25–40 kJ mol⁻¹ but also in a change in the reaction mechanism. Received 26 May 2002 / Accepted 26 July 2002 / Published online: 14 February 2003     

An overlap criterion for selection of core orbitals

 An overlap criterion is defined that connects the identification of core orbitals in a molecular system, which can be problematic, to that in isolated atoms, which is well defined. This approach has been tested on a variety of troublesome systems that have been identified in the literature, including molecules containing third-row main-group elements, and is shown to remove errors of up to 100 kcal/mol arising from an inconsistent treatment of core orbitals at different locations on a potential-energy surface. For some systems and choices of core orbitals, errors as large as 19 kcal/mol can be introduced even when consistent sets of orbitals are frozen, and the new method is shown to identify these cases of substantial core–valence mixing. Finally, even when there is limited core–valence mixing, the frozen-core approximation can introduce errors of more than 5 kcal/mol, which is much larger than the presumed accuracy of models such as G2 and CBS-QB3. The source of these errors includes interatomic core–core and core–valence dispersion forces. Received: 31 August 2001 / Accepted: 11 October 2001 / Published online: 9 January 2002     

Aconityl-derived polymers for biomedical applications. Modeling study of cis–trans isomerisation

 Soluble polymers have been prepared that are designed to undergo enhanced rates of hydrolysis at pH values less than that observed in blood circulation. The degradable element in the polymer mainchain is derived from cis-aconityl acid and is defined by a carboxylic acid pendent functionality (C-4) that is cis across a double bond to an amide at C-1 in the polymer mainchain. While degradation studies in vitro have confirmed these polymers do undergo enhanced rates of degradation at acidic pH values, there is also increasing evidence that during the degradation process the double bond isomerises to the trans configuration and thus prevents the full degradation of a polymer. From a molecular modelling perspective we are seeking to understand the propensity for this cis–trans isomerisation and the mechanism of this cis–trans isomerisation is discussed. Received: 29 April 2002 / Accepted: 6 September 2002 / Published online: 14 February 2003