Valence-bond determination of bond lengths of polycyclic aromatic hydrocarbons: comparisons with recent experimental and ab initio results

Pauling's valence-bond (VB) method for determining bond lengths is compared to ten recent literature experimental and theoretical results and is shown to give comparable results. His method only requires computation of the number of Kekulé (K) and Dewar structures (DS) of conjugated hydrocarbons. Both K and DS are obtained from the last two coefficients of the matching polynomial which is also used to obtain topological resonance energy (TRE). A molecular fragmentation method is given for determining DS of essentially disconnected polycyclic aromatic hydrocarbons (PAHs). Both Kekuléan alternant and nonalternant PAHs, including essentially disconnected and non-Kekuléan systems, have bond lengths that are easily determined by this method.     

Basis set dependence of ab initio geometry predictions for AB4 molecules

Theoretical predictions of AB₄ molecular structures are very sensitive to choice of basis set. This has been previously demonstrated for the SH₄ and SF₄ molecules. Here it is shown that while both minimum and double zeta basis sets predict ClF₄⁺ to have a C_4v structure, the addition of d functions on Cl results in a C_2v geometry, similar to the experimentally known structure of SF₄.     

The geometric and electronic structures of oxocarbons. An ab initio molecular orbital study

Ab initio molecular orbital calculations with the STO-3G and 4-31G basis sets have been carried out for the neutral oxocarbons C_nO_n (n = 3, 4, 5, 6 and 7), the dianions C_nO_n^2- (n = 3, 4, 5, 6 and 7), the monoanions C_nO_nH^? (n = 3 and 4) and the related acids C_nO_nH₂ (n = 3 and 4). Fully optimised geometries have been obtained for all species. The geometries, stabilities and acidities are discussed.     

Conformational properties and homolytic bond cleavage of organic peroxides. I. An empirical approach based upon molecular mechanics and ab initio calculations

The conformational features of a large number of hydroperoxides ROOH and peroxides ROOR′, where R and R′ are alkyl groups of different and increasing size and phenyl rings, including ortho substituted derivatives, were obtained from molecular mechanics calculations by employing a standard package. For the molecules of small molecular size, comparison was carried out with the results of ab initio calculations. Heats of formation were also obtained from molecular mechanics for hydroperoxides and peroxides: The values are, in general, overestimated. For the molecules containing the CF₃ group, the calculated values are subject to large errors and heats of formation were obtained from ab initio total energies in the “atom equivalents” scheme. To estimate the homolytic dissociation energies of the different bonds in the peroxide molecules, heats of formation of R·, ·OR, and ·OOR radicals were employed and several of them had to be calculated. Different approaches were employed—molecular mechanics calculations, ab initio energies within the atom equivalent and isodesmic reaction schemes, and Benson's group additivity rule; values consistent within the different calculation methods were chosen for estimating dissociation energies. The bond dissociation energies indicate different trends in these molecules as a function of the nature of the R and R′ groups and the possible electronic effects operating in these molecules are discussed. © 1993 John Wiley & Sons, Inc.     

An empirical potential for the O-H·O Hydrogen bond: Part I. Comparison with ab initio molecular orbital results

An empirical potential energy function has been devised for the O-H·O hydrogen bond, for use with the MMI force field. The energy of the hydrogen bond is described as the sum of van der Waals, electrostatic and Morse components. The function has been used to calculate the potential energy hypersurface of the water dimer, and the results are compared with published ab initio molecular orbital studies. Satisfactory agreement is obtained except for orientations involving very short H·H contacts. The geometry and hydrogen bond energy of the equilibrium linear form of (H₂O)₂ are calculated to be r(O·O) = 2.84 Å, θ = 36°, ΔE = ?5.35 kcal mol^?1, which are close to the values obtained by experiment, and from molecular orbital calculations. The relative importance of the electrostatic component of the empirical hydrogen bond energy is consistent with molecular orbital energy decomposition studies. The empirical function has also been used to calculate the energy of the water trimer in orientations which serve as models for the crystallographic bifurcated hydrogen bond. The results indicate that, in these orientations, the trimer is typically 0–3 kcal mol^?1 more stable than the dimer, a result which is consistent with ab initio calculations.     

Basis set effects and the choice of reference geometry in ab initio calculations of vibrational spectra

Tatewaki and Huzinaga's [J. Comput. Chem. 1 , 205 (1980)] basis sets, constructed to minimize superposition error, were used to calculate infrared (IR) frequencies and intensities. They were found inferior to Pople bases such as 3–21G and 6–31G*. The question of whether a theoretical vibrational spectrum should be computed at experimental or theoretical bond lengths was also investigated. If the magnitude of the correlation energy increases with bond length, Hartree-Fock bond lengths are expected to be shorter than experimental, and frequencies computed there will be higher than those computed at experimental lengths. Conversely, if this magnitude decreases with R, computed lengths should be longer than experimental and should give lower computed frequencies.     

Controlling the shape and flexibility of arylamides: a combined ab initio, ab initio molecular dynamics, and classical molecular dynamics study

Using quantum chemistry plus ab initio molecular dynamics and classical molecular dynamics methods, we address the relationship between molecular conformation and the biomedical function of arylamide polymers. Specifically, we have developed new torsional parameters for a class of these polymers and applied them in a study of the interaction between a representative arylamide and one of its biomedical targets, the anticoagulant drug heparin. Our main finding is that the torsional barrier of a C(aromatic)-C(carbonyl) bond increases significantly upon addition of an o-OCH2CH2NH3+ substituent on the benzene ring. Our molecular dynamics studies that are based on the original general AMBER force field (GAFF) and GAFF modified to include our newly developed torsional parameters show that the binding mechanism between the arylamide and heparin is very sensitive to the choice of torsional potentials. Ab initio molecular dynamics simulation of the arylamide independently confirms the degree of flexibility we obtain by classical molecular dynamics when newly developed torsional potentials are used.     

Refined ab initio 6-31G split-valence basis set optimization of the molecular structures of biphenyl in twisted,planar, and perpendicular conformations

Improved full ab initio optimizations of the molecular structure of biphenyl in twisted minimum energy, coplanar, and perpendicular conformations by use of Poles's GAUSSIAN 82 program have been performed in the 6-31G basis set. These lead to geometries and energies of much higher reliability than our earlier STO-3G results. The torsional angle Φ_min obtained now is 45.41° in close agreement with the recent experimental value of 44.4° ± 1.2°. Calculated CC distances may be converted to experimental ED r_g-values by means of independently determined linear regression correlations with very high statistical confidence, although they agree better with experimental x ray data for coplanar biphenyl without this correction. Calculated intramolecular angles are very similar for both STO-3G and 6-31G basis sets. The calculated torsional energy barrier towards Φ = 90° (ΔE⁹⁰) is 6.76 kJ/mol in close agreement with the experimental-31G value of 6.5 ± 2.0 kJ/mol. For coplanar biphenyl with D_2h-symmetry the calculated torsional energy barrier ΔE⁰ is 13.26 kJ/mol which is surprisingly much higher than the experimental value of 6.0 ± 2.1 kJ/mol. This discrepancy could not be resolved by optimizations assumed for two kinds of distortions of planarity of orthohydrogens from the molecular plane of the coplanar carbon atoms. But for the twisted minimum energy conformation asymmetric bending of ortho-H atoms lead to a torsional angle Φ_min = 44.74° together with a dihedral angle towards ortho-H of 1.22°, and consequently even to an increase of torsional energy barriers to ΔE⁰ = 13.51 and ΔE⁹⁰ = 6.91 kJ/mol.     

The ab initio calculated molecular structures,force fields and vibrational frequencies of some organic azides

Double zeta basis molecular calculations were carried out on the hydrazoic acid and azidomethane molecules. The molecular structures were optimized by the gradient method and the force fields were obtained by numerical differentiation of the gradient vector. The computed harmonic force fields and vibrational frequencies were compared with experimental values.     

The effects of fluorine and chlorine substitution on bond lengths in ethanes and disilanes: comparisons of ab initio and experimental information

Ab initio and some density functional theory calculations of bond lengths in fluoro- and chloro-ethanes and disilanes are reported with a precision of ±0.0001 Å under strictly comparable conditions. The resulting changes in MH and MX (M=C, Si; X=F, Cl) bond length are analysed for the effects of halogens substituted in geminal (), or vicinal (gauche or trans) positions. The shortening effect of halogen on an MH bond is markedly reduced or even reversed by the introduction of electron correlation at the MP2 or B3LYP level. MX bonds are little affected. gauche halogen consistently shortens both MH and MX bonds, while trans halogen has no effect on an MH bond but a small and variable effect on the MX bond.

The reality of these calculated changes in bond length is tested in two ways. MH bond lengths are plotted against experimental values of the isolated stretching frequencies ν^isMH, which themselves correlate well with experimental r₀ bond lengths. Agreement on the resulting substituent effects is generally good for the gauche and trans effects of halogen but variable for effects. Unobserved ν^isMH values are predicted from computed bond lengths in fluoroethanes, chloroethanes and chlorodisilanes.

Calculated MX and MM bond lengths are compared with experimental values, notably those from electron diffraction studies amongst the ethanes. Most calculations underestimate the changes found experimentally in CF and CCl bond lengths. CC bond length changes are underestimated in fluoroethanes and overestimated in the chloro-compounds.

The ‘offset’ value (r_e(calc)−r_e(true)) for a CH or SiH bond calculated with a given basis set and level of theory in most cases varies markedly throughout the series of compounds. The same is true for CF, CCl, CC and SiSi bonds if the corresponding offset values for the r_a lengths are constant.

The need is stressed for extended experimental work on many of the compounds, especially the disilanes. It is recommended that structures should be refined with ab initio derived constraints on the bond lengths involved and differences between spectroscopic and diffraction-based geometries reconciled through the calculation of r_z structures.     

Use of molecular dynamics simulations with ab initio SCF calculations for the determination of the deuterium quadrupole coupling constant in liquid water and bond lengths in ice

The deuterium quadrupole coupling constant and asymmetry parameter in heavy water were determined using ab initio SCF calculations. Snapshots from a molecular dynamics simulation were used to give liquid water cluster configurations and the influence of simulation parameters on the quadrupole coupling constant was investigated. The electronic potential model and the number of molecules in the molecular dynamics simulation and the pressure of the system were found to have only a small influence on the quadrupole coupling constant. The average value of the quadrupole coupling constant at room temperature, corrected for the known deficiency of the ab initio calculation in the gas phase, yields a quadrupole coupling constant of 253 kHz, in perfect agreement with the most recent experiments. The oxygen—deuterium bond lengths in ice Ih, ice II, and ice IX were determined using experimental quadrupole coupling constants and a model equation. An averaged bond length of 98.9 pm was obtained for the Ih form, which is approximately 2 pm shorter than that determined by neutron diffraction studies, whereas the bond lengths for the four deuterium sites in ice II and the three sites in ice IX are in fair agreement with experiment. © John Wiley & Sons, Inc.     

Insights into the structures, energetics, and vibrations of aqua-rubidium(I) complexes: ab initio study

We have carried out ab initio and density functional theory calculations of hydrated rubidium cations. The calculations involve a detailed evaluation of the structures, thermodynamic properties, and IR spectra of several plausible conformers of Rb+ (H2O)(n=1-8) clusters. An extensive search was made to find out the most stable conformers. Since the water-water interactions are important in hydrated Rb+ complexes, we investigated the vibrational frequency shifts of the OH stretching modes depending on the number of water molecules and the presence/absence of outer-shell water molecules. The predicted harmonic and anharmonic vibrational frequencies of the aqua-Rb+ clusters reflect the H-bonding signature, and would be used in experimental identification of the hydrated structures of Rb+ cation.     

The ab initio calculation of molecular electric, magnetic and geometric properties

We give an account of some recent advances in the development of ab initio methods for the calculation of molecular response properties, involving electric, magnetic, and geometric perturbations. Particular attention is given to properties in which the basis functions depend explicitly both on time and on the applied perturbations such as perturbations involving nuclear displacements or external magnetic fields when London atomic orbitals are used. We summarize a general framework based on the quasienergy for the calculation of arbitrary-order molecular properties using the elements of the density matrix in the atomic-orbital basis as the basic variables. We demonstrate that the necessary perturbed density matrices of arbitrary order can be determined from a set of linear equations that have the same formal structure as the set of linear equations encountered when determining the linear response equations (or time-dependent self-consistent-field equations). Additional components needed to calculate properties involving perturbation-dependent basis sets are flexible one- and two-electron integral techniques for geometric or magnetic-field differentiated integrals; in Kohn-Sham density-functional theory (KS-DFT), we also need to calculate derivatives of the exchange-correlation functional. We describe a recent proposal for evaluating these contributions based on automatic differentiation. Within this framework, it is now possible to calculate any molecular property for an arbitrary self-consistent-field reference state, including two- and four-component relativistic self-consistent-field wave functions. Examples of calculations that can be performed with this formulation are presented.     

Zwitterionic mechanisms for photooxygenation reactions of n-activated c-c double bonds: full geometry optimizations of the diradical and zwitterionic intermediates by ab initio SCF method

Geometry optimizations of perepoxide, 1,4-diradical, zwitterion and dioxetane for the 1,1-diaminoethylene plus singlet molecular oxygen system were performed using the energy gradients of the HF 4-31G and STO-3G solutions. The zwitterion (ZW) is more stable than the perepoxide and σπ-diradical (DR) intermediates (at the 4-31G level), supporting the previous ZW mechanism for photoovygenation reactions of N-activated C-C double bonds     

Complete basis set ab initio computational study of ionization potential, electron affinity and the C-F bond dissociation energy for perfluorinated methane derivatives

A computational study of perfluorinated methane derivatives was performed with complete basis set ab initio methods. The total energies for their neutral, cation, and anionic states were computed. From these values, the energy gaps between different electronic states, ionization potentials, electron affinities, and C-F bond dissociation energies were calculated. The computed values are compared with experimental data and the reliability of complete basis set ab initio methods is discussed. New values for C-F bond dissociation energies are suggested. Received: 12 January 1998 / Accepted: 2 April 1998 / Published online: 29 July 1998     

Investigation of possible structures of silicon nanotubes via density-functional tight-binding molecular dynamics simulations and ab initio calculations

We show, computationally, that single-walled silicon nanotubes (SiNTs) can adopt a number of distorted tubular structures, representing respective local energy minima, depending on the theory used and the initial models adopted. In particular, "gearlike" structures containing alternating sp(3)-like and sp(2)-like silicon local configurations have been found to be the dominant structural form for SiNTs via density-functional tight-binding molecular dynamics simulations (followed by geometrical optimization using Hartree-Fock or density function theory) at moderate temperatures (below 100 K). The gearlike structures of SiNTs deviate considerably from, and are energetically more stable than, the smooth-walled tubes (the silicon analogues of single-walled carbon nanotubes). They are, however, energetically less favorable than the "string-bean-like" SiNT structures previously derived from semiempirical molecular orbital calculations. The energetics and the structures of gearlike SiNTs are shown to depend primarily on the diameter of the tube, irrespective of the type (zigzag, armchair, or chiral). In contrast, the energy gap is very sensitive to both the diameter and the type of the nanotube.